Problem

Source: Turkey TST 2022 P4 Day 2

Tags: geometry, geometry proposed, circles, tangent circles



We have three circles w1, w2 and Γ at the same side of line l such that w1 and w2 are tangent to l at K and L and to Γ at M and N, respectively. We know that w1 and w2 do not intersect and they are not in the same size. A circle passing through K and L intersect Γ at A and B. Let R and S be the reflections of M and N with respect to l. Prove that A,B,R,S are concyclic.