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<APB+ <MPC=180

Source: 2023 Viet Nam math olympiad for high school students D1 P3

March 25, 2023
geometry

Problem Statement

Given a triangle ABCABC isosceles at A.A. A point PP lying inside the triangle such that ∠PBC=∠PCA\angle PBC=\angle PCA and let MM be the midpoint of BC.BC.
Prove that: ∠APB+∠MPC=180∘.\angle APB+ \angle MPC =180^{\circ}.
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