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2024 Geo Problem 1

Source:

April 15, 2024
geometry

Problem Statement

Let ABCDABCD be a rectangle with AB=5AB=5. Let EE be on AB‾\overline{AB} and FF be on CD‾\overline {CD} such that AE=CF=4AE=CF=4. Let PP and QQ lie inside ABCDABCD such that triangles AEPAEP and CFQCFQ are equilateral. If EE, PP, QQ, and FF lie on a single line, find BC‾\overline{BC}.
Proposed by Connor Gordon
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