Question 29
Let $ABCD$ be a trapezoid ($AB \parallel CD$) and denote $P = BC \cap AD$. Let $k_1, k_2$ be circles with diameters $BC, AD$, respectively, and denote $P = BC \cap AD$. Prove that the tangents from $P$ to $k_1$ form the same angle as the tangents from $P$ to $k_2$. (Patrik Bak)