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A line passing through the orthocenter, creating an angular bisector

Source: Baltic Way 2020, Problem 13

November 14, 2020
geometrygeometry proposed

Problem Statement

Let ABCABC be an acute triangle with circumcircle ω\omega. Let ℓ\ell be the tangent line to ω\omega at AA. Let XX and YY be the projections of BB onto lines ℓ\ell and ACAC, respectively. Let HH be the orthocenter of BXYBXY. Let CHCH intersect ℓ\ell at DD. Prove that BABA bisects angle CBDCBD.
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