Problem

Source: Switzerland - Swiss ΜΟ 2015 p8

Tags: geometry, trapezoid, concurrency, concurrent



Let $ABCD$ be a trapezoid, where $AB$ and $CD$ are parallel. Let $P$ be a point on the side $BC$. Show that the parallels to $AP$ and $PD$ intersect through $C$ and $B$ to $DA$, respectively.