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2020 PUMaC Geometry A1 / B3

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December 31, 2021
geometry

Problem Statement

Let γ1\gamma_1 and γ2\gamma_2 be circles centered at OO and P P respectively, and externally tangent to each other at point QQ. Draw point DD on γ1\gamma_1 and point EE on γ2\gamma_2 such that line DEDE is tangent to both circles. If the length OQ=1OQ = 1 and the area of the quadrilateral ODEPODEP is 520520, then what is the value of length PQPQ?
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