Let AB be an arbitrary chord of the circle (O). Two circles (X) and (Y) are on the same side of the chord AB such that they are both internally tangent to (O) and they are tangent to AB at C,D respectively, C is between A and D. Let H be the intersection of XY and AB,M the midpoint of arc AB not containing X and Y . Let HM meet (O) again at I. Let IX,IY intersect AB again at K,J. Prove that the circumcircle of triangle IKJ is tangent to (O).Nguyễn Văn Linh
tangent circlescirclesgeometry