Let AD be the bisector of triangle ABC. Circle ω passes through the vertex A and touches the side BC at point D. This circle intersects the sides AC and AB for the second time at points M and N respectively. Lines BM and CN intersect the circle for the second time ω at points P and Q, respectively. Lines AP and AQ intersect side BC at points K and L, respectively. Prove that KL=21BC equal segmentsgeometrycircleangle bisectorChampions Tournament