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Two circles with radii a and b touch eac...

Two circles with radii `a and b` touch each other externally such that `theta` is the angle between the direct common tangents, `(a > bgeq2)` . Then prove that `theta=2sin^(-1)((a-b)/(a+b))` .

A

`theta=sin^(-1)((r_(1)+r_(2))/(r_(1)-r_(2)))`

B

`theta=2sin^(-1)((r_(1)-r_(2))/(r_(1)+r_(2)))`

C

`theta=sin^(-1)((r_(1)-r_(2))/(r_(1)+r_(2)))`

D

None of these

Text Solution

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The correct Answer is:
B
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