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Existence of circle

Source: Latvian TST for Baltic Way 2020 P9

October 18, 2020
geometry

Problem Statement

Given △ABC\triangle ABC, whose all sides have different length. Point PP is chosen on altitude ADAD. Lines BPBP and CPCP intersect lines AC,ABAC, AB respectively and point X,YX, Y.It is given that AX=AYAX=AY. Prove that there is circle, whose centre lies on BCBC and is tangent to sides ACAC and ABAB at points X,YX,Y.
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