1. Given circles $\odot O_{1}$ and $\odot O_{2}$ intersect at points $A$ and $B$, with radii $5$ and $7$ respectively, and $O_{1} O_{2}=6$. A line through point $A$ intersects $\odot O_{1}$ and $\odot O_{2}$ at points $C$ and $D$, respectively. Points $P$ and $O$ are the midpoints of segments $CD$ and $O_{1} O_{2}$, respectively. Find the length of $OP$.
(Draw diameter $A E$ and $A F$ of $\odot O_{1}$ and $\odot O_{2}$ through point $A$, and extend $A O$ to intersect $E F$ at point $G$. Then $E, B, F$ are collinear, and $E F \parallel O_{1} O_{2}$. It is easy to see that $P G$ is the midline of the right trapezoid $C E F D$. $O P=\frac{1}{2} A G=A O=2 \sqrt{7}$. )