In the given 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 = 3.8 cm then the length of QR is

Question

Philoid · Accepted Answer

Let the bigger circle be C1 and Smaller be C2,

Now,

PQ and PT are two tangents to circle C1,

∴ PT = QP

[Tangents drawn from an external point are equal]

QP = 3.8 cm

[ As PT = 3.8 cm is given]

Also,

PR and PT are two tangents to circle C2,

∴ PT = PR

[Tangents drawn from an external point are equal]

PR = 3.8 cm

[ As PT = 3.8 cm is given]

QR = QP + PR = 3.8 + 3.8 = 7.6 cm