In triangle ABC, point I is the center, point Ia is the center of the excircle tangent to the side BC. From the vertex A inside the angle BAC draw rays AX and AY. The ray AX intersects the lines BI, CI, BIa, CIa at points X1, ..., X4, respectively, and the ray AY intersects the same lines at points Y1, ..., Y4 respectively. It turned out that the points X1,X2,Y1,Y2 lie on the same circle. Prove the equality X3X4X1X2=Y3Y4Y1Y2. excentergeometryratioConcyclicUkrainian TYM