Question 128
Segment $AB$ is $20~\mathrm{cm}$ long and point $O$ is its midpoint. Circle $\mathcal{K}$ is externally tangent to the circles with diameters $AO$ and $BO$ and internally tangent to the circle with diameter $AB$ (see the figure). How many centimetres is the radius of circle $\mathcal{K}$?
(A) $\frac{5}{2}$
(B) $\frac{10}{3}$
(C) $\frac{5 \sqrt{2}}{2}$
(D) $\sqrt{5}$
(E) $2 \sqrt{5}$
(A) $\frac{5}{2}$
(B) $\frac{10}{3}$
(C) $\frac{5 \sqrt{2}}{2}$
(D) $\sqrt{5}$
(E) $2 \sqrt{5}$