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AB is a line segment of length 48 cm and...

AB is a line segment of length 48 cm and C is its mid-point. If three semicircles are drawn at AB, AC and CB using as diameters, then radius of the circle inscribed in the space enclosed by three semicircles is

A

`3sqrt(2)`

B

6

C

8

D

10

Text Solution

Verified by Experts

The correct Answer is:
C

In `DeltaXCO`, we have
`OX^(2) +XC^(2) +OC^(2)`
`rArr (12+r)^(2) = 12^(2) +(24 -r)^(2)`
`rArr r =8`
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