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2021 Geo Div 1 P1 (Div 2 P2)

Source:

March 2, 2021
geometry

Problem Statement

Points AA, BB, and CC lie on a line, in that order, with AB=8AB=8 and BC=2BC=2. BB is rotated 20∘20^\circ counter-clockwise about AA to a point B′B', tracing out an arc R1R_1. CC is then rotated 20∘20^\circ clockwise about AA to a point C′C', tracing out an arc R2R_2. What is the area of the region bounded by arc R1R_1, segment B′CB'C, arc R2R_2, and segment C′BC'B?
Proposed by Thomas Lam
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