Question 74
Let $ABC$ be a non-isosceles triangle with centroid $G$ and inscribed in circle $(O)$. Let $M, N, P$ be the midpoints of $BC, CA, AB$ respectively. Let $D, E, F$ be the reflection points of the foot of the internal bisector of angles $A, B, C$ through $M, N, P$ respectively. Prove that the orthocenter of triangle $DEF$ lies on line $OG$.