A triangle has side lengths of 10, 24, and 26. Let a be the area of the circumcircle. Let b be the area of the incircle. Compute a - b.
The triangle is a right-angled triangle.
Radius of circumcircle = 26/2 = 13
Area of circumcircle = π⋅132=169π
Radius of incircle = 2×AreaPerimeter=4
Area of incircle = π⋅42=16π
Therefore a−b=169π−16π=153π
Because this is a right triangle (102 + 242 = 262), the center of the circumcircle is the midpoint of the
hypotenuse. This means that the radius of the circumcircle = 26/2 = 13.
Because this is a right triangle, the radius of the incircle can be found using this formula:
r = ( a + b - c ) / 2 where c is the hypotenuse and a and b are the other two sides.
From these radii, you can calculate the areas.