2017 AMC 12A Problems/Problem 16

Problem

In the figure below, semicircles with centers at $A$ and $B$ and with radii 2 and 1, respectively, are drawn in the interior of, and sharing bases with, a semicircle with diameter $JK$ . The two smaller semicircles are externally tangent to each other and internally tangent to the largest semicircle. A circle centered at $P$ is drawn externally tangent to the two smaller semicircles and internally tangent to the largest semicircle. What is the radius of the circle centered at $P$ ?

$\textbf{(A)}\ 3/4 \qquad \textbf{(B)}\ 6/7 \qquad\textbf{(C)}\ 1/2 * sqrt3 \qquad\textbf{(D)}\ 5/8 * sqrt2 \qquad\textbf{(E)}\ 11/12$

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2017 AMC 12A Problems/Problem 16

Problem