Problem

Source: India tst 2002 p13

Tags: Asymptote, geometry, circumcircle, geometric transformation, reflection, trapezoid, perpendicular bisector



Let $ABC$ and $PQR$ be two triangles such that (a) $P$ is the mid-point of $BC$ and $A$ is the midpoint of $QR$. (b) $QR$ bisects $\angle BAC$ and $BC$ bisects $\angle QPR$ Prove that $AB+AC=PQ+PR$.