Question 118
Let $ABC$ be a triangle and let $D$ be a point on the segment $BC$, $D \neq B$ and $D \neq C$. The circle $ABD$ meets the segment $AC$ again at an interior point $E$. The circle $ACD$ meets the segment $AB$ again at an interior point $F$. Let $A'$ be the reflection of $A$ in the line $BC$. The lines $A'C$ and $DE$ meet at $P$, and the lines $A'B$ and $DF$ meet at $Q$.
Prove that the lines $AD$, $BP$ and $CQ$ are concurrent (or all parallel).
Prove that the lines $AD$, $BP$ and $CQ$ are concurrent (or all parallel).