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Sum of angles are equal

Source: China Mathematical Olympiad 2021 P4

November 25, 2020
geometryChina MO2021P4

Problem Statement

In acute triangle ABC(AB>AC)ABC (AB>AC), MM is the midpoint of minor arc BCBC, OO is the circumcenter of (ABC)(ABC) and AKAK is its diameter. The line parallel to AMAM through OO meets segment ABAB at DD, and CACA extended at EE. Lines BMBM and CKCK meet at PP, lines BKBK and CMCM meet at QQ. Prove that ∠OPB+∠OEB=∠OQC+∠ODC\angle OPB+\angle OEB =\angle OQC+\angle ODC.
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