Question 8
Let $ABC$ be a triangle. Denote by $P$ the reflection of $B$ in $(AC)$ and by $Q$ the reflection of $C$ in $(AB)$.
Let $T$ be the intersection of $(PQ)$ with the tangent at $A$ to the circumcircle of $(APQ)$.
Show that the reflection of $T$ in $A$ lies on $(BC)$.
Let $T$ be the intersection of $(PQ)$ with the tangent at $A$ to the circumcircle of $(APQ)$.
Show that the reflection of $T$ in $A$ lies on $(BC)$.