Question 2
Let $(O)$ be a circle and $A$ a point outside it. Draw tangents $AB,AC$, with points of contact $B,C$. Let $P$ lie on the ray opposite to $BA$ and $Q$ on the ray opposite to $CA$, so that $PQ$ is tangent to $(O)$. The line through $P$ parallel to $AC$ meets line $BC$ at $E$; the line through $Q$ parallel to $AB$ meets line $BC$ at $F$.
1. Prove that $QE$ and $PF$ pass through fixed points $M$ and $N$, respectively.
2. Prove that $PM\cdot QN$ is constant.
Editorial correction: The source accidentally calls $A,B$ the points of contact; these must be $B,C$.
1. Prove that $QE$ and $PF$ pass through fixed points $M$ and $N$, respectively.
2. Prove that $PM\cdot QN$ is constant.
Editorial correction: The source accidentally calls $A,B$ the points of contact; these must be $B,C$.