Problems(1)
Given a scalene triangle ABC inscribed in the circle (O). Let (I) be its incircle and BI,CI cut AC,AB at E,F respectively. A circle passes through E and touches OB at B cuts (O) again at M. Similarly, a circle passes through F and touches OC at C cuts (O) again at N. ME,NF cut (O) again at P,Q. Let K be the intersection of EF and BC and let PQ cuts BC and EF at G,H, respectively. Show that the median correspond to G of the triangle GHK is perpendicular to IO. geometry