Problem

Source: OMEC Ecuador National Olympiad Final Round 2023 N3 P2 day 1

Tags: geometry, national olympiad, geometric transformation, reflection



Let $ABCD$ a cyclic convex quadrilateral. There is a line $l$ parallel to $DC$ containing $A$. Let $P$ a point on $l$ closer to $A$ than to $B$. Let $B'$ the reflection of $B$ over the midpoint of $AD$. Prove that $\angle B'AP = \angle BAC$