Question 22
Let $ABC$ be an acute non-isosceles triangle and inscribed in circle $(O)$ with the $A$-symmedian intersecting $(O)$ again at $D$. Let $G$ be a point symmetrical to $A$ through $BC$. Suppose $GB, GC$ intersect $(O)$ respectively at $E, F$. The inscribed circle of triangle $AEF$ touches $EF$ at $J$.
1. Prove that $GO, GD$ are symmedians of triangles $GAD$ and $GEF$.
2. Prove that the two rays $AJ, AD$ are symmetric respect to $AG$.
1. Prove that $GO, GD$ are symmedians of triangles $GAD$ and $GEF$.
2. Prove that the two rays $AJ, AD$ are symmetric respect to $AG$.