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For the triangle below, let x be the area of the circumcircle, and let y be the area of the incircle. Compute x-y

Sorry, I couldn't include the triangle but in the triangle, there is a side with length 42, length 58, and length 40. It is a right triangle with the ninetey degree angle on angle C and the side CB is 40 units long, AC is 42 units long, and BA is 58 units long. I hope this is enough infomation because I really need to know how to do this so can someone help explain how to do this. I need to learn with an explanation instead with just the answer.

Dec 15, 2021
edited by Guest  Dec 15, 2021

#1
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Well, this took a buttload of work but I finally managed to figure it out. The answer is 697 pi :)

Dec 16, 2021
#2
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The center of the circumcircle of a right triangle is the midpoint of the hypotenuse.

This makes the radius of the circumcircle one-half the diameter = 58 / 2  =  29.

The area of the circumcircle is  pi · 292  =  841 · pi

By a well-known theorem (a polite way to say "look it up"), the radius of the incircle of a right triangle is found

by adding the two sides together, subtracting the hypotenuse and then dividing this answer by 2.

The radius of the incircle is (40 + 42 - 58) / 2  =  12

The area of the incircle is  pi · 122  =  144 · pi