2021 Fall AMC 12B Problem 22

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

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.