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In the following diagram, a semicircle o...

In the following diagram, a semicircle of radius r inscribes two semicircles, which are tangent to each other at a point B on the diameter AC of the larger semicircle. Then there is a full circle inscribed in the remaining area, which is tangent to all the three existing semicircles. Find the radius of this full circle, if the diameter AB=1/3 cm and BC=2/3 cm.

A

A) 2/15 cm

B

B) 1/7 cm

C

C) 1/9 cm

D

D) none of these

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A
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