For the triangle below, let x be the area of the circumcircle, and let y be the area of the incircle. Compute x−y.
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
+1348 
