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Two circles with radii a and b(agtb) tou...

Two circles with radii a and b(agtb) touch each other externally . Let c be the radii of a circle both touches these two circles as well as a direct common tangent to these two circles. Then

A

`1/(sqrt(r_(3)))=1/(sqrt(r_(1)))+1/(sqrt(r_(2))`

B

`1/(sqrt(r_(3)))=|1/(r_(1))-1/(sqrtr_(2))|`

C

`sqrt(r_(3))-sqrt(r_(1))+sqrt(r_(2))`

D

`sqrt(r_(3))=|sqrt(r_(1))-sqrt(r_(2))|`

Text Solution

Verified by Experts

The correct Answer is:
A
Using length of direct common tangent
`{:(PQ^(2),=,4r_(1)r_(2)),(QR^(2),=, 4r_(1)r_(3)):}|=PQ=PR+QR`
`implies1/(sqrt(r_(3)))=1/(sqrt(r_(1)))+1/(sqrt(r_(2)))`
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