IMO 1974 LL BUL4

Origin: BUL

Problem

Let Ka, Kb, Kc with centers Oa, Ob, Oc be the excircles of a triangle ABC, touching the interiors of the sides BC, CA, AB at points Ta, Tb, Tc respectively. Prove that the lines OaTa, ObTb, OcTc are concurrent in a point P for which POa = POb = POc = 2R holds, where R denotes the circumradius of ABC. Also prove that the circumcenter O of ABC is the midpoint of the segment PJ, where J is the incenter of ABC.