MathDB

Equilateral triangle

ABC

has side length

2

. A semicircle is drawn with diameter

BC

such that it lies outside the triangle, and minor arc

BC

is drawn so that it is part of a circle centered at

A

. The area of the “lune” that is inside the semicircle but outside sector

ABC

can be expressed in the form

\sqrt{p}-\frac{q\pi}{r}

, where

p, q

, and

r

are positive integers such that

q

and

r

are relatively prime. Compute

p + q + r

. https://cdn.artofproblemsolving.com/attachments/7/7/f349a807583a83f93ba413bebf07e013265551.png

Problem Statement