1. Triangle $G R T$ has $G R=5, R T=12$, and $G T=13$. The perpendicular bisector of $G T$ intersects the extension of $G R$ at $O$. Find $T O$.
Answer: $\square$
First, note that $T O=G O$ as $O$ lies on the perpendicular bisector of $G T$. Then if $M$ is the midpoint of $G T$, we have that $\triangle G R T \sim \triangle G M O$, so we can compute $T O=G O=G M \cdot \frac{G T}{G R}=\frac{13}{2} \cdot \frac{13}{5}=\frac{169}{10}$.