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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 $x - y.$

 

 Dec 18, 2023
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The altitude =   sqrt (3)/2 *a

 

The circumradius =   (2/3)sqrt (3)/2 a  = (1/sqrt3) a

The inradius = (1/3)sqrt (3) / 2 )a = (sqrt (3) / 6) a =   (1/ ( 2sqrt 3) a 

 

x  -  y  =      pi   [ ( 1/sqrt3 * a)^2 - ( 1/ (2sqrt 3) * a)^2 ] =   a^2/4

 

 

cool cool cool

 Dec 19, 2023

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