Let ABCD be a quadrilateral inscribed in a circle k. Let the lines AC∩BD=O, AD∩BC=P, and AB∩CD=Q. Line QO intersects k in points M and N. Prove that PM and PN are tangent to k.
Problem
Source: II International Festival of Young Mathematicians Sozopol 2011, Theme for 10-12 grade
Tags: geometry, quadrilateral, tangency