Question

In Fig. two equal circles touch each other at T, if QP = 4.5 cm, then QR =

A. 9 cm 

B. 18 cm 

C. 15 cm 

D. 13.5 cm

Answer 1

Answer is A. 9 cm

Given: 

QP = 4.5 cm 

Property: 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 the above property, 

PQ = PT = PR = 4.5 cm (tangent from P) 

Now, 

QR = PQ + PR 

QR = PQ + PQ [∵PQ = PR] 

QR = 2PQ 

QR = 2 × 4.5 cm

QR = 9 cm 

Hence, QR = 9 cm