Let ABC be a triangle with circumcirle Γ, and let M and N be the respective midpoints of the minor arcs AB and AC of Γ. Let P and Q be points such that AB=BP, AC=CQ, and P, B, C, Q lie on BC in that order. Prove that PM and QN meet at a point on Γ.Proposed by Victor Domínguez geometryarc midpointcircumcircle