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Question
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
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.
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