Question 132
Points $B,D$ lie on a circle $\omega$. The tangents at $B,D$ meet at $P$. A line through $P$ meets $\omega$ at $A,C$. Let $\ell$ be any line parallel to $BD$ that intersects the polygonal lines $ABC$ and $ADC$. Prove that $\ell$ divides the lengths of those two polygonal lines in the same ratio. (L. Emelyanov)