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2013 preRMO p12, computational with equilateral and rectangle

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August 8, 2019
geometryrectangleEquilateral

Problem Statement

Let ABCABC be an equilateral triangle. Let PP and SS be points on ABAB and ACAC, respectively, and let QQ and RR be points on BCBC such that PQRSPQRS is a rectangle. If PQ=3PSPQ = \sqrt3 PS and the area of PQRSPQRS is 28328\sqrt3, what is the length of PCPC?
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