Question 79
Let $\mathcal{K}$ be the circumcircle of the acute triangle $ABC$ with $|AB| \lt |AC|$. Let $p$ be the reflection of the line $BC$ over the line $AB$. The line $p$ intersects the circle $\mathcal{K}$ at $B$ and $E$. The tangent to $\mathcal{K}$ at $A$ intersects the line $p$ at $D$. Let $F$ be the reflection of the point $D$ over the point $A$. The line $CF$ intersects the circle $\mathcal{K}$ at $C$ and $G$. Prove that the lines $CE$ and $GB$ are parallel.