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Lots of perpendiculars

Source: Poland 73-3-1

March 31, 2022
geometry

Problem Statement

Let ABCABC be an acute triangle with AB<ACAB<AC. The angle bisector of BACBAC intersects the side BCBC and the circumcircle of ABCABC at DD and M≠AM\neq A, respectively. Points XX and YY are chosen so that MX⊥ABMX \perp AB, BX⊥MBBX \perp MB, MY⊥ACMY \perp AC, and CY⊥MCCY \perp MC. Prove that the points X,D,YX,D,Y are collinear.
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