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 \overline{J K}. 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 ?
Answer Choices
A. \dfrac{3}{4}
B. \dfrac{6}{7}
C. \dfrac{1}{2} \sqrt{3}
D. \dfrac{5}{8} \sqrt{2}
E. \dfrac{11}{12}