Problem

Source: Azerbaijan Math Olympiad Training

Tags: geometry, TST



Consider two circles k1,k2 touching at point T. A line touches k2 at point X and intersects k1 at points A,B where B lies between A and X.Let S be the second intersection point of k1 with XT. On the arc \overarcTS not containing A and B , a point C is choosen. Let CY be the tangent line to k2 with Yk2 , such that the segment CY doesn't intersect the segment ST .If I=XYSC , prove that : (a) the points C,T,Y,I are concyclic. (b) I is the Aexcenter of ABC