Let $ABCD$ be a convex quadrilateral with $\angle B= \angle D$. Prove that the midpoint of $BD$ lies on the common internal tangent to the incircles of triangles $ABC$ and $ACD$.
Source: Sharygin 2022 Finals 10-11.4
Tags: geometry
Let $ABCD$ be a convex quadrilateral with $\angle B= \angle D$. Prove that the midpoint of $BD$ lies on the common internal tangent to the incircles of triangles $ABC$ and $ACD$.