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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.

 Jun 29, 2020
 #1
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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. 

169pi-16pi=153pi 

 Jun 29, 2020
 #2
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tysm! this really helped! 

Guest Jun 29, 2020

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