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CM \perp DN

Source: Tuymaada 2024 Juniors P6

July 10, 2024
geometry

Problem Statement

Extension of angle bisector BLBL of the triangle ABCABC (where AB<BCAB < BC) meets its circumcircle at NN. Let MM be the midpoint of BLBL. Isosceles triangle BDCBDC with base BCBC and angle equal to ABCABC at DD is constructed outside the triangle ABCABC. Prove that CM⊥DNCM \perp DN. Proposed by А. Mardanov
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