In figure, QR is a common tangent to the given circles, touching externally at the point T.
The tangent at T meets QR at P. If PT = 3.8cm, then find the length of QR

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Solution

Lengths of the tangents drawn from an external point to a circle are equal.

$∴ Q P = P T = 3.8 c m . . . . . . . . . . . . (i)$

$P R = P T = 3.8 c m . . . . . . . . . . . . (i i)$

From equations (i) and (ii):

$Q P = P R = 3.8 c m$

But, $Q R = Q P + P R$

$∴ Q R = 3.8 + 3.8$

$Q R = 7.6 c m$

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