+1248 For the triangle below, let $x$ be the area of the circumcircle, and let $y$ be the area of the incircle. Compute $x - y.$
+129771 c/ sin (105) = 7/ sin (35)
c = 7sin (105) / sin (35) ≈ 11.8
a / sin ( 40 ) = 7/sin (35)
a = 7 sin (40) / sin (35) ≈ 7.8
Semi-perimeter of triangle = (7 + 11.8 + 7.8) / 2 = 13.3 = S
Area of triangle sqrt [ 13.3 (13.3- 11.8)(13.3 - 7.8) (13.3 - 7) ] ≈ 26.3 = A
Incircle radius = A / S = 26.3 / 13.3 ≈ 1.98
Circumcircle radius = abc / ( 4A) = (7 * 7.8 * 11.8) / [4 * 26.3 ] ≈ 6.12
x - y = pi ( 6.12^2 - 1.98^2) ≈ 105.35
