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2016 CNMO Grade 10 P2

Source: 2016 China Northern MO Grade 10, Problem 2

February 24, 2020
geometry

Problem Statement

In isosceles triangle ABCABC, ∠CAB=∠CBA=α\angle CAB=\angle CBA=\alpha, points P,QP,Q are on different sides of line ABAB, and ∠CAP=∠ABQ=β,∠CBP=∠BAQ=γ\angle CAP=\angle ABQ=\beta,\angle CBP=\angle BAQ=\gamma. Prove that P,C,QP,C,Q are colinear.
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