Let $ABC$ be an acute triangle. Let $D$ be a point on the line parallel to $AC$ that passes through $B$, such that $\angle BDC = 2\angle BAC$ as well as such that $ABDC$ is a convex quadrilateral. Show that $BD + DC = AC$.
Source: KAMO 2022 Grade 9 P2
Tags: geometry, rectangle
Let $ABC$ be an acute triangle. Let $D$ be a point on the line parallel to $AC$ that passes through $B$, such that $\angle BDC = 2\angle BAC$ as well as such that $ABDC$ is a convex quadrilateral. Show that $BD + DC = AC$.
