Let ABCDEF be a convex hexagon with sides not parallel and tangent to a circle Γ at the midpoints P, Q, R of the sides AB, CD, EF respectively. Γ is tangent to BC, DE and FA at the points X,Y,Z respectively. Line AB intersects lines EF and CD at points M and N respectively. Lines MZ and NX intersect at point K. Let r be the line joining the center of Γ and point K. Prove that the intersection of PY and QZ lies on the line r. geometryhexagonconcurrencyconcurrent