Circles k1 and k2 intersect at points M and N. The line ℓ intersects the circle k1 at points A and C, the circle K2 at points B and D so that the points A,B,C and D lie on the line ℓ are in that order. Let X a point on the line MN such that the point M is located between the points X and N. Let P be the intersection of lines AX and BM, and Q be the intersection of lines DX and CM. If K is the midpoint of segment AD and L is the midpoint of segment BC, prove that the lines XK and ML intersect on the line PQ. concurrencyconcurrentgeometrycircles