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.
This is a right triangle.
The circumcircle of a right triangle has its diameter as the hypotenuse. The diameter is 26, therefore the radius is 13. The area of the circumcircle is 13^2pi.
The incircle's radius is 1/2(a+b-c), where a and b are the legs of the triangle and c is the hypotenuse. So the radius is 1/2(10+24-26)=4.
The area of the incircle is 4^2pi.