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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 10, 2020
 #1
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a - b = 144*pi - 16*pi = 128*pi.

 Jun 10, 2020
 #2
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thx :D

 Jun 10, 2020
 #3
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its incorrect but thx anyway

 Jun 10, 2020
 #4
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+2

We know that this is a right triangle

 

To find the circumcircle radius, we can just divide the hypotnuse of the triangle by 2, or 26/2 = 13, as the hypotnuse passes through the center of the circle. 


To find the incircle radius, it is (leg1 + leg2 - hypotnuse)/2, or (10+24-26)/2 = 4

 

Hope this helps you :D

 

 

 

 

 

 

 

 

 

 

 

 

 

13^2 - 4^2pi= 169pi-16pi = 153pi     :)

 Jun 11, 2020

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