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find point, equal angles, parallelogram related (HOMC 2008 Q9)

Source:

July 25, 2019
geometryparallelogramequal anglesconstruction

Problem Statement

Consider a triangle ABCABC. For every point M ∈BC\in BC ,we define N∈CAN \in CA and P∈ABP \in AB such that APMNAPMN is a parallelogram. Let OO be the intersection of BNBN and CPCP. Find M∈BCM \in BC such that ∠PMO=∠OMN\angle PMO=\angle OMN
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