2. Point $P$ and line $\ell$ are such that the distance from $P$ to $\ell$ is 12 . Given that $T$ is a point on $\ell$ such that $P T=13$, find the radius of the circle passing through $P$ and tangent to $\ell$ at $T$.
Answer: $169 / 24$ Let $O$ be the center of the given circle, $Q$ be the foot of the altitude from $P$ to $\ell$, and $M$ be the midpoint of $P T$. Then since $O M \perp P T$ and $\angle O T P=\angle T P Q, \triangle O M P \sim \triangle T Q P$. Thus the $O P=T P \cdot \frac{P M}{P Q}=13 \cdot \frac{13 / 2}{12}=\frac{169}{24}$