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In a geometry problem, why is the concept of semi-perimeter important?
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It's used in various formulas to find in-radii and areas of triangles.
How can the in-radius (r) be calculated using the area and semi-perimeter of the triangle?
In-radius (r) = (Area of the triangle) / (Semi-perimeter)
How is the distance between two points calculated using the Pythagorean theorem?
Distance = √(Δx² + Δy²)
What is the general formula for the area of a triangle?
Area = 0.5 * base * height or (in-radius * semi-perimeter)
In a right-angle triangle with sides 15, 20, and 25, how is BD calculated?
Using the Pythagorean theorem, BD = 9
How to find the distance between the in-centers of triangles formed in a rectangle with sides 9 and 12?
Using the Pythagorean theorem, the distance = 3√5
How is the semi-perimeter (s) of a triangle calculated?
Semi-perimeter (s) = (Sum of all sides) / 2
In the equation 2A + 7C = 9B with A = 12, how do you find C?
C = 25.5
What is the sum of the in-radii of triangles ABD and ADB given the sides 15, 20, and 25?
7
Given the area of a right-angle triangle is 80 square units and its perimeter is 80 units, what is the length of the hypotenuse?
38 units
What formula is used to find the in-radius (r) of a triangle?
How is the height of a right-angle triangle calculated if the area is 150 square units and the base is 25?
Height = 12
How can the hypotenuse of a right-angled triangle be found if the sides are known?
Using the Pythagorean theorem, c² = a² + b²
What is a Pythagorean triplet?
A set of three integers that satisfy a² + b² = c²
Calculate the area of a triangle with a circumradius of 18 and an in-radius of 8.
352 square units
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