In Fig. 1, 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

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#### Solution

It is known that the length of the tangents drawn from an external point to a circle are equal.

∴ QP = PT = 3.8 cm ...(1)

PR = PT = 3.8 cm ...(2)

From equations (1) and (2), we get:

QP = PR = 3.8 cm

Now, QR = QP + PR

= 3.8 cm + 3.8 cm

= 7.6 cm

Hence, the correct option is B.

Concept: Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles

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