2021 Fall AMC 12B Problems/Problem 22

Problem

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 $OP$ ?

$\textbf{(A)}\ \frac{23}{8} \qquad\textbf{(B)}\ \frac{29}{10} \qquad\textbf{(C)}\ \frac{35}{12} \qquad\textbf{(D)}\ \frac{73}{25} \qquad\textbf{(E)}\ 3$

Solution

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~Wilhelm Z

2021 Fall AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 21	Followed by Problem 23
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All AMC 12 Problems and Solutions

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2021 Fall AMC 12B Problems/Problem 22

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