Track / Stage 4 / 169 of 340 #429 of 2000

Problem 429

AMC 12 late, AIME early

Geometry Difficulty 4.8 Find the answer

18. A circle with center $C$ and radius $r$ intersects the square $E F G H$ at $H$ and at $M$ , the midpoint of $E F$ . If $C, E$ and $F$ are collinear and $E$ lies between $C$ and $F$ , what is the area of the region outside the circle and inside the square in terms of $r$ ?

Your answer

Official solution

18. $r^{2}\left(\frac{22}{25}-\frac{\tan ^{-1}(4 / 3)}{2}\right)$

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.