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Find the angles of triangle ABC

Source: 2022 Bulgarian Spring Math Competition, Problem 11.2

March 27, 2022
geometrylengths

Problem Statement

A circle through the vertices AA and BB of △ABC\triangle ABC intersects segments ACAC and BCBC at points PP and QQ respectively. If AQ=ACAQ=AC, ∠BAQ=∠CBP\angle BAQ=\angle CBP and AB=(3+1)PQAB=(\sqrt{3}+1)PQ, find the measures of the angles of △ABC\triangle ABC.
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