Right triangle $ABC$ has side lengths $BC=6$, $AC=8$, and $AB=10$. A circle centered at $O$ is tangent to line $BC$ at $B$ and passes through $A$. A circle centered at $P$ is tangent to line $AC$ at $A$ and passes through $B$. What is $OP$? $\textbf{(A)}\ \frac{23}{8} \qquad$ $\textbf{(B)}\ \frac{29}{10} \qquad$ $\textbf{(C)}\ \frac{35}{12} \qquad$ $\textbf{(D)}\ \frac{73}{25} \qquad$ $\textbf{(E)}\ 3$