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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))` .

Text Solution

Verified by Experts

From `Delta MLN`,
`sin .(theta)/(2) =(a-b)/(a+b)`
or `(theta)/(2)=sin^(-1)((a-b)/(a+b))`
Therefore, the angle between AB and AD is
`theta = 2 sin ^(-1)((a-b)/(a+b))`
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