Question

In Fig. 8.78, there are two concentric circles with centre O. PRT and PQS are tangents to the inner circle from a point P lying on the outer circle. If PR = 5 cm, find the length of PS.

Answer 1

Given that PR = 5 cm.
PR and PQ are the tangents to the inner circle so,
PR = PQ = 5 cm                                (Tangents drawn from an external point to the circle are equal)
Now draw a perpendicular from the centre O to the tangent PS.
PS is the chord of the inner circle. we know that the perpendicular drawn
from the centre of the circle to the chord bisects the chord. So, PQ = QS = 5 cm
PS = PQ + QS = 5 cm + 5 cm = 10 cm