Problem

Source: II International Festival of Young Mathematicians Sozopol 2011, Theme for 10-12 grade

Tags: geometry, quadrilateral, tangency



Let ABCD be a quadrilateral inscribed in a circle k. Let the lines ACBD=O, ADBC=P, and ABCD=Q. Line QO intersects k in points M and N. Prove that PM and PN are tangent to k.