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2020 PUMaC Geometry A3 / B5

Source:

December 31, 2021
geometry

Problem Statement

Let ABCDABCD be a cyclic quadrilateral with circumcenter OO and radius 1010. Let sides ABAB, BCBC, CDCD, and DADA have midpoints M,N,PM, N, P, and QQ, respectively. If MP=NQMP = NQ and OM+OP=16OM + OP = 16, then what is the area of triangle △OAB\vartriangle OAB?
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