Q.Let ABC be a triangle with X, Y, and Z as excenters. Prove that triangle XYZ has orthocenter I and that triangle ABC is its orthic triangle.
I am able to prove that ZBAI,XBIC and YCIA are cyclic by using excenter lemma. Then I can say that IB, IC and IA are the radical axes of (ZBAI)&(XBIC), (XBIC)&(YCIA), (ZBAI)&(YCIA) respectively. But after this I got stuck...kindly help me
