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

Answer 1

The correct option is B

7.6

It is known that the length of the tangent drawn from an external point to a circle is equal.
$\therefore$ 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.