Question

In Fig.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

Answer is B. 7.6

Given: 

PT = 3.8 cm 

Property 1: If two tangents are drawn to a circle from one external point, then their tangent segments (lines joining the external point and the points of tangency on circle) are equal. 

By property 1, 

PQ = PT (Tangent from P) 

PR = PT (Tangent from P) 

Now, 

QR = PQ + PR 

⇒ QR = PT + PT 

⇒ QR = 3.8 cm + 3.8 cm 

⇒ QR = 7.6 cm 

Hence, QR = 7.6 cm