MathDB
Equal angles in a parallelogram

Source: 2022 IZHO P3, https://izho.kz/contest/problems/

February 18, 2022
geometryparallelogramequal angles

Problem Statement

In parallelogram ABCDABCD with acute angle AA a point NN is chosen on the segment ADAD, and a point MM on the segment CNCN so that AB=BM=CMAB = BM = CM. Point KK is the reflection of NN in line MDMD. The line MKMK meets the segment ADAD at point LL. Let PP be the common point of the circumcircles of AMDAMD and CNKCNK such that AA and PP share the same side of the line MKMK. Prove that ∠CPM=∠DPL\angle CPM = \angle DPL.
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