In parallelogram ABCD, point K is marked on diagonal AC. Circle s1 passes through point K and touches lines AB and AD (s1 intersects the diagonal AC for the second time on the segment AK). Circle s2 passes through point K and touches lines CB and CD (s2 intersects for the second time diagonal AC on segment KC). Prove that for all positions of the point K on the diagonal AC, the straight lines connecting the centers of circles s1 and s2, will be parallel to each other. geometryparallelparallelogram