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 (in cm) is

(a) 3.8 (b) 7.6 (c) 5.7 (d) 1.9 [CBSE 2014]

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Solution

It is given that QR is a common tangent to the given circles touching externally at the point T. Also, the tangent at T meets QR at P such that PT = 3.8 cm.

Now, PQ and PT are tangents drawn to the same circle from an external point P.

∴ PQ = PT = 3.8 cm (Lengths of tangents drawn from an external point to a circle are equal)

PR and PT are tangents drawn to the same circle from an external point T.

∴ PR = PT = 3.8 cm (Lengths of tangents drawn from an external point to a circle are equal)

Now,

QR = PQ + PR = 3.8 cm + 3.8 cm = 7.6 cm

Thus, the length of QR is 7.6 cm.

Hence, the correct answer is option B.

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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 (in cm) is (a) 3.8 (b) 7.6 (c) 5.7 (d) 1.9 [CBSE 2014]

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(a) 3.8 (b) 7.6 (c) 5.7 (d) 1.9 [CBSE 2014]