Geometry Practice Class Notes

[Music] [Music] yeah hi everyone my name is Ari Prakash and we're going to practice class of geometry okay so we'll start with this question we'll do some fantastic questions in this few practice classes very important concepts you will do okay this very very borned one this very good question okay just see this question one of the sides of an optic obtuse angle angle of 30 meter one it is centimeter is it's intimate okay so it is an obtuse angle as you select random okay so obtuse angle absolute triangle of parameter 180 centimeter is it is in centimeter so it is one of the sides okay what is the distance between in center and circumcenter this transit so we solve it see now say since it is an obtuse angle triangle so we need we know the condition for updos and will gradually write what is the condition of condition for obtuse angle triangle it was long each side square right if you remove it it is long each side square should be greater than sum of squares of sum of squares of other two sides long each side square should be rather than sum of squares of other two sides okay this is the condition for up to assemble travel so if one side of it Randall is 180 centimeter right if one side is one it is sorry one play with pay middle for it one it is a demeter and one set is 80 centimeter we can have to infer information from you right what are the first thing the first thing we can have is see the first thing we can have is a triangle with side 80 80 and 20 because if one side is as 80 centimeter so it's an isosceles triangle right so two sides are equal this one is 80 so other would also be 80 this is one case okay and second cases second case is this one if one is AP then red two will be right - two are equal no say one is 80 so 100 is left so 100 is left so 100 as 50 and 50 okay so again that means one side is 50 this side is 50 and this side is beauty okay so this is there are two cases so eighty eighty twenty fifty fifty eighty fine so you see here long each side square should be greater than sum square some other two side that means this obviously here 80 square is greater than fifty square plus fifty square in second case it is proved here eighty square will not be greater than eighty square plus 20 squared it becomes false right it is not true that means that means the sides of our triangular 80 50 and 50 okay so very important information sides of a triangular 80 50 and 55 now they solve it now will solve it okay okay the sides of our triangular that we got here is 80 50 and 50 correct now let's make let's make it so a triangle a triangle with eighty fifty eight fifty sighs okay the triangle with so resistivity yep this 50 this 50 and this is 80 so in a strangled the base is the 80 here so if you drop a perpendicular bit from you okay so if we read it this perpendicular acts as median as as well as the height of crandall that means this will become 40 this will become 40 it is 80 or this full number ok this full length this forty and forty if it is 40 it is 50 so by Pythagoras theorem it becomes 30 tried it becomes thirty right so this is 30 40 and 50 to define in center and set of tintin so for finding in center area is equal to R into this that we know okay so what is the in center of the triangle where is the incentive the triangle lights okay area equal to R into this what is the area here areas of triangle is what half into base into height so height is here is 30 be here is full ad okay so half into 30 into 80 is equal to R into S what is s here same perimeter that is half of 180 say favorite perimeter is half of 180 right so half of 180 that is 90 so we got to be got here should be 9mm yeah sorry this will be 90 M so this will be 90 is 30 will cancel out 33 times so we got our R is equal to R is equal to 160 by 3 that is 53 point D okay so in radiuses fifty three point three three right dude at this point here in radius is 53 points with you okay so if any radius is 53.3 its Yodas enough circumradius we can also calculate circumradius right you can also calculate circumradius so for calculating circumradius will calculate again area is equal to ABC by four are correct ABC by 4 okay notice area here we've got area same thing your area is half into 30 into 80 if we see are the four sides that is 80 into 50 into ABC are the three sides it 80 50 and 50 upon fold on okay now again cancer here okay this comes to 50 right no cancel out 25 + 25 - so what we're left here is R is equal to 25 into 25 by 15 further guy has it 5 by 3 it becomes 125 by 3 okay so R becomes 125 by 3 that is that is 41 point six six to circumradius becomes forty one point six six any radius becomes R it is 50/50 so in words so Katherine we take out the near I think yeah I'm sorry 160 by three once hpy three it will become not one city by three eighty it becomes 40 here 40 by 3 so it becomes not one city very to those 40 by 3 that is 13.33 okay so some definitely take okay so R is equal to thirteen point three three you got capital R is equal to 14 or forty one point six six we got dizzy okay so now observe the situation here we got small R is equal to thirteen point three three and we got capital R is equal to forty one point six six okay so also what is this case here okay we will observe what is just case here okay see the next Li C capital R we got as thirteen point three so it's smaller that is in radius we got a thirteen point three three capital R we got as forty one point six six current now this isn't Rann million of those is a triangle here okay this is a triangle so triangle ABC is a triangle ABC here so R is equal to thirteen point three three fine so C so shatral is fifty it was fifty into a perpendicular it was forty and it was forty okay so this somewhere here it would be cerca this circumradius is basically distance of circum distance of circumcenter from the vertex right circumradius is distance of circumcenter from the vertex okay this is a vertex here so what is the vertex a here okay this is a vertex a so from here it is it it is at a distance of forty one point six six so since this is 30 so obviously do you go beyond it right the name is a CD ad will go beyond ad to 30 and plus eleven point six inch so let's say this is the circumcenter okay let's it is a circumcenter ste and this length is 30 plus eleven point should be eleven point six six to make it full forty one point six six correct what is inner radius in Iridessa 13.33 what is actually in radius from in center it is distance of distance of the perpendicular drawn from the vertex on that side right if you remember in radius in circle this is insulting this is in center but is in radius length of this perpendicular drawn since in radians okay so in this case this is a perpendicular on here so let's say that somewhere in center would be here I okay and it is at a distance of 13.33 from the deep this distance is what it did it is this 13.33 from D this distance is 13.33 from B from D okay this is a two point three three so called total version was what is the distance between in center and circumcenter so in center and circumcenter that length the distance between I and C I want but if visible it is here thirteen point three three plus eleven point six six okay thirteen point three three plus eleven point six six it becomes 25 okay that is thirteen point three three distance between in center and circumcenter is equal to thirteen point three three plus eleven point six six that is 25 25 is the answer okay it should be twenty four point nine nine but we have assumed after it was 125 by three and forty one forty sorry this is 60 by three this capital R was 125 by three and it's a small R was 40 by 3 if you calculate after in fractions not in recurring decimal you did put 425 only right 13 points 83 plus their inputs itsuka - ready comes when it prettier is the answer very good question very good concentrate push it okay no they don't next question fill tube in question okay so this is a next question here in this question see in this question will see this o a and OB are the tangent to the circle okay and OB is equal to 2 0 4 and AP is equal to 102 Oh a business straight line joining to this point of contact of the tangent here so AP is equal to 1 at you to o P equal to 0 for we defined a length of radius of the circle okay so radius means I need to find it just join a P so I need to find the length of a P here ok so how to find it ok so see how does are very very good questions very nice question how to solve it here so we can't think we have it ready to consort of kites in circle okay we have Astrid into concepts of kites in circles so kites in circle basically what two tangents and two radius in a circle all it forms a kite right we did this see yes circle here so two tangents and two radius in a circle or a sponsor criteria center here okay this let's say Oh a OB are the tangents if I join P so P a P we are the radius so it it is a kite because PA and PB are equal because of being radius o a is equal to Kobe because of me tangent okay so pay o equal to Bobby because of being tangent right so it follow the property of kite so what are the properties of idea so we've learned it if I join a B that is a shorter dagger of the guide and if I join Oh B that is a longer Daniel dazzle of the kite okay so in this case this this let's say this point is Q here this a Q is equal to Q B because we've studied it longer delay in a kite longer diagonal in a kite bisects the shorter diagonal longer diagonal in a guide biceps the shorter Dagenham okay that means that means this is PA okay this is a radius if I join this PB here it also radius so I taken right here that Oh a PB o a PB forms a kind right Oh a PB forms a kind into right this here that o APB forms a kite so if oFPP forms a kite here for all in our body of sight so a B is the longer than of this special a b is the shorter data of this side and Opie is the longer diagonal of this type okay so if a B is 192 so it just started that long short long red Avenel bite six shorter diagonal at a ninety degree this is a property of quiet okay longer diagonal bisects shorter diagonal at 90 degree so this bicep means these two will be equal so if hole is one and you do so half of it right so half will be 96 96 okay and then we also know that from point of from a point length of both the tangents drawn on this circular equal that means mu P will be equal to oay if it is to 0 for this also becomes 2 0 4 correct okay so now we need to find the length of your this AP or BB and if anything I need to find a length here let this point of contact where X ok this is X and this is also 90 degree because radius and tangent already is an angle of 90 degree so how to find a length of B B they go to many ways of finding right but I'll use the front of similarity because we studied it similarity similarity if you remember Z P B if I draw this red triangle outside okay make it clearly visible this is a triangle here so this is a P okay this is X okay this is B this is o this is 90 degree and this is also 90 degree this is also 90 degree okay so basically it is a right angle triangle PB ho and BX is a perpendicular so again his 90 degree so you can use fund of similarity that trip right angle inside a right angle triangle okay so we have you showing it both the triangles are similar if you drink in if you take any three pairs of triangle here right both the small one okay or one bigger one and one is more this is small one and when this bigger or and is a small one okay so all three pairs of transits has similar here we were shredded this okay so what I do here is to finding the length of her this VP I'll use front of similarity okay so we know that we know that triangle we know that triangle p XB is similar to triangle XB o okay we write on the basis of angle we don't write on the basis of here order here px and xB and xB and X oh right so it doesn't matter whatever is the order right because we are reading similarity in the business of and there's not on the basis of this ordering of this px be or sides of or the vertex of this little angles okay so it doesn't matter you so this P xB is here XB o is here okay and so what to do i assume any one angle as theta this is 90 this becomes 90 minus theta okay and this is the whole 90 this becomes theta this is 90 this is Theta this becomes 90 minus theta that's why we written this both triangle is similar because of a a similarity for a similarity we need only two angles okay but here all three angles are equal that's a plus point for us so these two triangles are similar okay so these two travelers similar what length is known this length is 2:04 fine okay what is this length this length is 96 fine so by Pythagoras theorem okay this is 96 this then this X B's and it is okay this XV is 96 xB is 96 so xB is 96 okay this bo is to 0-4 we need to find the length of oh it's this we can do by Pythagoras theorem okay but directly we can do we don't need to do that much also we know that what is the ratio of sides here to 0-4 is the hypotenuse so to 0-4 is 296 what are the ratio sides if you cancel out - L will go eight times here - every go 17 times here so this is a ratio of sides is 17 each to it okay so if you're have a pattern interpret it is quite easy if this is 17 if this is 8 this have to be 15 okay because PI throw spider underplayed to do it very fast ok 17 8 and 15 or if you got this to a 7 and it by Patterson this will get X X OS 15 so you'll get this X Oh Oh XS 15 X Oh or OSS you'll get as 15 okay so once you get is 15 what is the multiplying factor for this triplet so it is 8 into 296 it is 17 into 12 rows 2 0 4 so it will be it will be 15 into 12 it will be 180 therefore o X is 180 okay o X is 180 ob is to 0 for X B is 96 in this triangle it is not known okay so we'll calculate assess this vp's the radius this we need to gather this BP is the radius radius of the circle BP is the radius of the circle this we need to calculate okay so now let's do it let's do it 78 okay now so if these two triangles are similar now so take take any angle so we need our air so if I need are here I will pick 90 if I need our air I will pick 90 here in this triangle 90 in triangle pxb 90 a positives are in triangle x OB 90 a positive 2 0 force ratio becomes R upon 2 0 4 is equal to one more you take so you have to pick from with this angle you have to bid 90 mess it up you won't be theta because theta poet is not known so what will be cured with 90 minus theta so if you build a team as it up in this triangle 90 minus theta opposite is 96 and in this triangle 90 minus theta poet is 180 it is 180 yes the bushes all okay then they simply cancel it out sir 12 will go 15 times 12 is or 17 times okay now 96 by 15 has every year 5 and this will be 32 so R becomes 32 into 17 by 5 if calculation will take is not there no but is that ok 1750 yeah fine 32 it is hurting by fives if you solve it double 8/10 so you get a ballot 32 into 34 for 3234 is how much it is 33 square minus 1 so 1088 by 10 it is 1 0 8 point 8 that should be the answer for this question okay so so sorry yeah fine this should be answer this question okay so hope you got it so this is a very good question to tangent of circle were given we need to find a length of radius a circle where this a B was given as ma'am 192 and OB was given at 2:04 so what we did we just joined this a b and it becomes a PB o or o a PB becomes a kite we know that in any circle two tangent and two radius forms a kind didn't follow all the properties of find the most basic property of the guide is longer diagonal bisects shorter diagonal at D 9 vice at the 90-degree okay so here the longer diagonal is OB shorter is AV advise it's a be at 90 degree so AV was 1 and u 2 in between that is 96 then you applied Pythagoras theorem to find the value of Oh X ok we got it as 2 0 sorry we got got it as 180 then we applied since both triangles are similar we applied to find out right angle triangle inside a degenerate triangle we were shut it is intuitive many times okay right angle triangle inside right angle triangle okay so this is applied similarity and we got the value of our formula okay so hope it is clear okay see you nation thank you you [Music]

[Music] [Music] yeah hi everyone my name is Ari Prakash and we&#39;re going to practice class of geometry okay so we&#39;ll start with this question we&#39;ll do some fantastic questions in this few practice classes very important concepts you will do okay this very very borned one this very good question okay just see this question one of the sides of an optic obtuse angle angle of 30 meter one it is centimeter is it&#39;s intimate okay so it is an obtuse angle as you select random okay so obtuse angle absolute triangle of parameter 180 centimeter is it is in centimeter so it is one of the sides okay what is the distance between in center and circumcenter this transit so we solve it see now say since it is an obtuse angle triangle so we need we know the condition for updos and will gradually write what is the condition of condition for obtuse angle triangle it was long each side square right if you remove it it is long each side square should be greater than sum of squares of sum of squares of other two sides long each side square should be rather than sum of squares of other two sides okay this is the condition for up to assemble travel so if one side of it Randall is 180 centimeter right if one side is one it is sorry one play with pay middle for it one it is a demeter and one set is 80 centimeter we can have to infer information from you right what are the first thing the first thing we can have is see the first thing we can have is a triangle with side 80 80 and 20 because if one side is as 80 centimeter so it&#39;s an isosceles triangle right so two sides are equal this one is 80 so other would also be 80 this is one case okay and second cases second case is this one if one is AP then red two will be right - two are equal no say one is 80 so 100 is left so 100 is left so 100 as 50 and 50 okay so again that means one side is 50 this side is 50 and this side is beauty okay so this is there are two cases so eighty eighty twenty fifty fifty eighty fine so you see here long each side square should be greater than sum square some other two side that means this obviously here 80 square is greater than fifty square plus fifty square in second case it is proved here eighty square will not be greater than eighty square plus 20 squared it becomes false right it is not true that means that means the sides of our triangular 80 50 and 50 okay so very important information sides of a triangular 80 50 and 55 now they solve it now will solve it okay okay the sides of our triangular that we got here is 80 50 and 50 correct now let&#39;s make let&#39;s make it so a triangle a triangle with eighty fifty eight fifty sighs okay the triangle with so resistivity yep this 50 this 50 and this is 80 so in a strangled the base is the 80 here so if you drop a perpendicular bit from you okay so if we read it this perpendicular acts as median as as well as the height of crandall that means this will become 40 this will become 40 it is 80 or this full number ok this full length this forty and forty if it is 40 it is 50 so by Pythagoras theorem it becomes 30 tried it becomes thirty right so this is 30 40 and 50 to define in center and set of tintin so for finding in center area is equal to R into this that we know okay so what is the in center of the triangle where is the incentive the triangle lights okay area equal to R into this what is the area here areas of triangle is what half into base into height so height is here is 30 be here is full ad okay so half into 30 into 80 is equal to R into S what is s here same perimeter that is half of 180 say favorite perimeter is half of 180 right so half of 180 that is 90 so we got to be got here should be 9mm yeah sorry this will be 90 M so this will be 90 is 30 will cancel out 33 times so we got our R is equal to R is equal to 160 by 3 that is 53 point D okay so in radiuses fifty three point three three right dude at this point here in radius is 53 points with you okay so if any radius is 53.3 its Yodas enough circumradius we can also calculate circumradius right you can also calculate circumradius so for calculating circumradius will calculate again area is equal to ABC by four are correct ABC by 4 okay notice area here we&#39;ve got area same thing your area is half into 30 into 80 if we see are the four sides that is 80 into 50 into ABC are the three sides it 80 50 and 50 upon fold on okay now again cancer here okay this comes to 50 right no cancel out 25 + 25 - so what we&#39;re left here is R is equal to 25 into 25 by 15 further guy has it 5 by 3 it becomes 125 by 3 okay so R becomes 125 by 3 that is that is 41 point six six to circumradius becomes forty one point six six any radius becomes R it is 50/50 so in words so Katherine we take out the near I think yeah I&#39;m sorry 160 by three once hpy three it will become not one city by three eighty it becomes 40 here 40 by 3 so it becomes not one city very to those 40 by 3 that is 13.33 okay so some definitely take okay so R is equal to thirteen point three three you got capital R is equal to 14 or forty one point six six we got dizzy okay so now observe the situation here we got small R is equal to thirteen point three three and we got capital R is equal to forty one point six six okay so also what is this case here okay we will observe what is just case here okay see the next Li C capital R we got as thirteen point three so it&#39;s smaller that is in radius we got a thirteen point three three capital R we got as forty one point six six current now this isn&#39;t Rann million of those is a triangle here okay this is a triangle so triangle ABC is a triangle ABC here so R is equal to thirteen point three three fine so C so shatral is fifty it was fifty into a perpendicular it was forty and it was forty okay so this somewhere here it would be cerca this circumradius is basically distance of circum distance of circumcenter from the vertex right circumradius is distance of circumcenter from the vertex okay this is a vertex here so what is the vertex a here okay this is a vertex a so from here it is it it is at a distance of forty one point six six so since this is 30 so obviously do you go beyond it right the name is a CD ad will go beyond ad to 30 and plus eleven point six inch so let&#39;s say this is the circumcenter okay let&#39;s it is a circumcenter ste and this length is 30 plus eleven point should be eleven point six six to make it full forty one point six six correct what is inner radius in Iridessa 13.33 what is actually in radius from in center it is distance of distance of the perpendicular drawn from the vertex on that side right if you remember in radius in circle this is insulting this is in center but is in radius length of this perpendicular drawn since in radians okay so in this case this is a perpendicular on here so let&#39;s say that somewhere in center would be here I okay and it is at a distance of 13.33 from the deep this distance is what it did it is this 13.33 from D this distance is 13.33 from B from D okay this is a two point three three so called total version was what is the distance between in center and circumcenter so in center and circumcenter that length the distance between I and C I want but if visible it is here thirteen point three three plus eleven point six six okay thirteen point three three plus eleven point six six it becomes 25 okay that is thirteen point three three distance between in center and circumcenter is equal to thirteen point three three plus eleven point six six that is 25 25 is the answer okay it should be twenty four point nine nine but we have assumed after it was 125 by three and forty one forty sorry this is 60 by three this capital R was 125 by three and it&#39;s a small R was 40 by 3 if you calculate after in fractions not in recurring decimal you did put 425 only right 13 points 83 plus their inputs itsuka - ready comes when it prettier is the answer very good question very good concentrate push it okay no they don&#39;t next question fill tube in question okay so this is a next question here in this question see in this question will see this o a and OB are the tangent to the circle okay and OB is equal to 2 0 4 and AP is equal to 102 Oh a business straight line joining to this point of contact of the tangent here so AP is equal to 1 at you to o P equal to 0 for we defined a length of radius of the circle okay so radius means I need to find it just join a P so I need to find the length of a P here ok so how to find it ok so see how does are very very good questions very nice question how to solve it here so we can&#39;t think we have it ready to consort of kites in circle okay we have Astrid into concepts of kites in circles so kites in circle basically what two tangents and two radius in a circle all it forms a kite right we did this see yes circle here so two tangents and two radius in a circle or a sponsor criteria center here okay this let&#39;s say Oh a OB are the tangents if I join P so P a P we are the radius so it it is a kite because PA and PB are equal because of being radius o a is equal to Kobe because of me tangent okay so pay o equal to Bobby because of being tangent right so it follow the property of kite so what are the properties of idea so we&#39;ve learned it if I join a B that is a shorter dagger of the guide and if I join Oh B that is a longer Daniel dazzle of the kite okay so in this case this this let&#39;s say this point is Q here this a Q is equal to Q B because we&#39;ve studied it longer delay in a kite longer diagonal in a kite bisects the shorter diagonal longer diagonal in a guide biceps the shorter Dagenham okay that means that means this is PA okay this is a radius if I join this PB here it also radius so I taken right here that Oh a PB o a PB forms a kind right Oh a PB forms a kind into right this here that o APB forms a kite so if oFPP forms a kite here for all in our body of sight so a B is the longer than of this special a b is the shorter data of this side and Opie is the longer diagonal of this type okay so if a B is 192 so it just started that long short long red Avenel bite six shorter diagonal at a ninety degree this is a property of quiet okay longer diagonal bisects shorter diagonal at 90 degree so this bicep means these two will be equal so if hole is one and you do so half of it right so half will be 96 96 okay and then we also know that from point of from a point length of both the tangents drawn on this circular equal that means mu P will be equal to oay if it is to 0 for this also becomes 2 0 4 correct okay so now we need to find the length of your this AP or BB and if anything I need to find a length here let this point of contact where X ok this is X and this is also 90 degree because radius and tangent already is an angle of 90 degree so how to find a length of B B they go to many ways of finding right but I&#39;ll use the front of similarity because we studied it similarity similarity if you remember Z P B if I draw this red triangle outside okay make it clearly visible this is a triangle here so this is a P okay this is X okay this is B this is o this is 90 degree and this is also 90 degree this is also 90 degree okay so basically it is a right angle triangle PB ho and BX is a perpendicular so again his 90 degree so you can use fund of similarity that trip right angle inside a right angle triangle okay so we have you showing it both the triangles are similar if you drink in if you take any three pairs of triangle here right both the small one okay or one bigger one and one is more this is small one and when this bigger or and is a small one okay so all three pairs of transits has similar here we were shredded this okay so what I do here is to finding the length of her this VP I&#39;ll use front of similarity okay so we know that we know that triangle we know that triangle p XB is similar to triangle XB o okay we write on the basis of angle we don&#39;t write on the basis of here order here px and xB and xB and X oh right so it doesn&#39;t matter whatever is the order right because we are reading similarity in the business of and there&#39;s not on the basis of this ordering of this px be or sides of or the vertex of this little angles okay so it doesn&#39;t matter you so this P xB is here XB o is here okay and so what to do i assume any one angle as theta this is 90 this becomes 90 minus theta okay and this is the whole 90 this becomes theta this is 90 this is Theta this becomes 90 minus theta that&#39;s why we written this both triangle is similar because of a a similarity for a similarity we need only two angles okay but here all three angles are equal that&#39;s a plus point for us so these two triangles are similar okay so these two travelers similar what length is known this length is 2:04 fine okay what is this length this length is 96 fine so by Pythagoras theorem okay this is 96 this then this X B&#39;s and it is okay this XV is 96 xB is 96 so xB is 96 okay this bo is to 0-4 we need to find the length of oh it&#39;s this we can do by Pythagoras theorem okay but directly we can do we don&#39;t need to do that much also we know that what is the ratio of sides here to 0-4 is the hypotenuse so to 0-4 is 296 what are the ratio sides if you cancel out - L will go eight times here - every go 17 times here so this is a ratio of sides is 17 each to it okay so if you&#39;re have a pattern interpret it is quite easy if this is 17 if this is 8 this have to be 15 okay because PI throw spider underplayed to do it very fast ok 17 8 and 15 or if you got this to a 7 and it by Patterson this will get X X OS 15 so you&#39;ll get this X Oh Oh XS 15 X Oh or OSS you&#39;ll get as 15 okay so once you get is 15 what is the multiplying factor for this triplet so it is 8 into 296 it is 17 into 12 rows 2 0 4 so it will be it will be 15 into 12 it will be 180 therefore o X is 180 okay o X is 180 ob is to 0 for X B is 96 in this triangle it is not known okay so we&#39;ll calculate assess this vp&#39;s the radius this we need to gather this BP is the radius radius of the circle BP is the radius of the circle this we need to calculate okay so now let&#39;s do it let&#39;s do it 78 okay now so if these two triangles are similar now so take take any angle so we need our air so if I need are here I will pick 90 if I need our air I will pick 90 here in this triangle 90 in triangle pxb 90 a positives are in triangle x OB 90 a positive 2 0 force ratio becomes R upon 2 0 4 is equal to one more you take so you have to pick from with this angle you have to bid 90 mess it up you won&#39;t be theta because theta poet is not known so what will be cured with 90 minus theta so if you build a team as it up in this triangle 90 minus theta opposite is 96 and in this triangle 90 minus theta poet is 180 it is 180 yes the bushes all okay then they simply cancel it out sir 12 will go 15 times 12 is or 17 times okay now 96 by 15 has every year 5 and this will be 32 so R becomes 32 into 17 by 5 if calculation will take is not there no but is that ok 1750 yeah fine 32 it is hurting by fives if you solve it double 8/10 so you get a ballot 32 into 34 for 3234 is how much it is 33 square minus 1 so 1088 by 10 it is 1 0 8 point 8 that should be the answer for this question okay so so sorry yeah fine this should be answer this question okay so hope you got it so this is a very good question to tangent of circle were given we need to find a length of radius a circle where this a B was given as ma&#39;am 192 and OB was given at 2:04 so what we did we just joined this a b and it becomes a PB o or o a PB becomes a kite we know that in any circle two tangent and two radius forms a kind didn&#39;t follow all the properties of find the most basic property of the guide is longer diagonal bisects shorter diagonal at D 9 vice at the 90-degree okay so here the longer diagonal is OB shorter is AV advise it&#39;s a be at 90 degree so AV was 1 and u 2 in between that is 96 then you applied Pythagoras theorem to find the value of Oh X ok we got it as 2 0 sorry we got got it as 180 then we applied since both triangles are similar we applied to find out right angle triangle inside a degenerate triangle we were shut it is intuitive many times okay right angle triangle inside right angle triangle okay so this is applied similarity and we got the value of our formula okay so hope it is clear okay see you nation thank you you [Music]

Transcript for:Geometry Practice Class Notes

Transcript for:
Geometry Practice Class Notes