`AB` is a line segment of length `2a`, with `M` as mid-point. Semi-circles are drawn on one side with `AM, MB` and `AB

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Q 1750256114.     `AB` is a line segment of length `2a`, with `M` as
mid-point. Semi-circles are drawn on one side
with `AM, MB` and `AB` as diameter as shown in the
figure. `A` circle with centre `O` and radius `r` is drawn such
that this circle touches all the three semi-circles. The
value of `r` is
CDS 2015 Paper-2
A

`(2a)/3`

B

`a/2`

C

`a/3`

D

`a/4`

HINT


Solution
(Provided By a Student and Checked/Corrected by EXXAMM.com Team)

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