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AB is a line segment with P as midpoint. Three semicircles are drawn with AP,PB and AB as diameters. Another circle is drawn so as to touch all three semicircles. What’s the radius of this smaller circle?

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AB is a line segment with P as midpoint. Three semicircles are drawn with AP,PB and AB as diameters. Another circle is drawn so as to touch all three semicircles. What’s the radius of this smaller circle?



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