Question

In Fig. 10.93, there are two concentric circles with centre O. PR and PQS are tangents to the inner circle from point plying on the outer circle. If PR = 7.5 cm, then PS is equal to
A. 10 cm
B. 12 cm
C. 15 cm
D. 18 cm

Answer 1

In Fig. 10.93, there are two concentric circles with centre O. PR and PQS are tangents to the inner circle from point plying on the outer circle. If PR = 7.5 cm, then PS is equal to 15 cm.

Option C is correct.

Construction: Join OQ and  OR

From figure it's clear that,

OR = OQ

PQ = PR ..........(1)

(as the tangents are from same circle to another same circle)

and we have,

PQ = QS ...........(2)

from (1) and (2), we have,

PR = QS

∴ PS = PQ + QS

PR = 7.5 cm (given)

PS = PR + PR

= 7.5 + 7.5

∴ PS = 15 cm.