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Prove that two angles are equal in an isosceles triangle

Source: XVII Sharygin Correspondence Round P8

March 2, 2021
geometry

Problem Statement

Let ABCABC be an isosceles triangle (AB=BCAB=BC) and ℓ\ell be a ray from BB. Points PP and QQ of ℓ\ell lie inside the triangle in such a way that ∠BAP=∠QCA\angle BAP=\angle QCA. Prove that ∠PAQ=∠PCQ\angle PAQ=\angle PCQ.
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