Question 6
Let $\Gamma$ be a circle with center $O$, and $(d)$ a line that does not intersect $\Gamma$. Let $P$ be the orthogonal projection of $O$ onto $(d)$. Let $Q$ be a variable point on the line $(d)$, and let $\left(t_{1}\right)$ and $\left(t_{2}\right)$ be the tangents to $\Gamma$ through $Q$. Let $A$ and $B$ be the orthogonal projections of $P$ onto $\left(t_{1}\right)$ and $\left(t_{2}\right)$. Show that the intersection point of $(AB)$ and $(OP)$ remains fixed as $Q$ varies.