Problem

Source: Germany 2016 - BWM Round 1, #3

Tags: geometry, geometry unsolved, perpendicular, circle, chord, Germany



Let $A,B,C$ and $D$ be points on a circle in this order. The chords $AC$ and $BD$ intersect in point $P$. The perpendicular to $AC$ through C and the perpendicular to $BD$ through $D$ intersect in point $Q$. Prove that the lines $AB$ and $PQ$ are perpendicular.