A diameter AK is drawn for the circumscribed circle ω of an acute-angled triangle ABC, an arbitrary point M is chosen on the segment BC, the straight line AM intersects ω at point Q. The foot of the perpendicular drawn from M on AK is D, the tangent drawn to the circle ω through the point Q, intersects the straight line MD at P. A point L (different from Q) is chosen on ω such that PL is tangent to ω. Prove that points L, M and K lie on the same line. geometrycircumcirclecollinear