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prove DBC is equal to ACD and BCM

Source: Sharygin Finals 2023 10.1

August 2, 2023
geometrySharygin Geometry OlympiadSharygin 2023

Problem Statement

Let MM be the midpoint of cathetus ABAB of triangle ABCABC with right angle AA. Point DD lies on the median ANAN of triangle AMCAMC in such a way that the angles ACDACD and BCMBCM are equal. Prove that the angle DBCDBC is also equal to these angles.
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