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Three congruent lines connected with right-angled triangle and its bisector

Source: IV Caucasus Mathematic Olympiad

April 7, 2019
geometry

Problem Statement

In a triangle ABCABC with ∠BAC=90∘\angle BAC = 90^{\circ} let BLBL be the bisector, L∈ACL\in AC. Let DD be a point symmetrical to AA with respect to BLBL. Let MM be the circumcenter of ADCADC. Prove that CMCM, DLDL, and ABAB are concurrent.
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