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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 11, 2020
 #1
avatar+9675 
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The triangle is a right-angled triangle.

 

Radius of circumcircle = 26/2 = 13

 

Area of circumcircle = π132=169π

 

Radius of incircle = 2×AreaPerimeter=4

 

Area of incircle = π42=16π

 

Therefore ab=169π16π=153π

 Jun 11, 2020
 #2
avatar+23254 
+1

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.

 Jun 11, 2020

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