hello and welcome to teen topics where you'll be taught all you need to know about Circle theorems so a circle theorem is basically finding the angle within a circle which has another shape inside it these shapes are generally not drawn to scale which makes it that little bit more difficult but don't worry in the next few minutes you will learn all you need to know about Circle theorems okay starting off a chord is a line that lies anywhere below the diameter that goes from one side to the other of the circle in this image the perpendicular bis sector of the cord passes through the center of the circle number two here we have a semicircle say we put another one on top and put a random triangle inside this half and name these angles a b and c then this angle B will become 90° but this is no fluke even if we have this triangle instead or maybe even this one they will always be 90° in fact put any triangle here and it will still add up to yep 90° number three a tangent is a line that passes the outside edge of a circle when this line is touched by the radius that means the angle will be 90° number four a subtended angle is almost like our eyesight when we look at an object our vision is focused on that taking this tree and this man for instance the subtended angle is 22° the subtended angle is basically the line Arc or object opposite to the inner triangle number five angles in the same segment subtended by the same Arc are equal for example ABC is the same as ADC number six when you have an Arro head shape inside a circle the inner angle here is twice this angle at the circumference number seven the diagram shows a silic lateral which is a four-sided shape with all of the its Corners touching the circumference what is different about this is that the opposite angles both add up to 180° so A and C would add up to 180 and B and D same thing number eight going back to the tangents if you do not remember go back to number three then the length of the two tangents would equal the same amount to explain that with a visual guide length AB is the same as AC [Music] number nine the angle between a tangent and a chord is equal to the angle in the alternate segment this is also known as an alternate segment theorem here was quite confusing looking sum that you are likely to get in a math exam have a look at this image and have a go can you do it pause the video and see what you can [Music] get okay so the sum we would do is a = 180 - 70 divide this all by two and this will equal 55° as some people already know the base of isoceles triangles will always equal now we get the 90 at angle B and take 55 which equals 35° how was I able to get this 90° well as previously explained when a radius and a tangent meet this creates a 90° Angle now we have 35° from the previous answer we times that by two to get 70 now we take it away from 180° finally we divide that 110 by 2 to give us 55° this is the angle marked D congratulations if this was your answer if there is anything you do not quite understand give me a shout out in the comments down below and I will happily answer your question if you found it interesting or helpful then maybe consider pressing that free little subscribe button down below it really helps me out a lot [Music]