Question

Q.6. In the figure, the radii of the two concentric circles are 17 cm and 10 cm. A line PQRS cuts the larger circle at P and S and the smaller circle at Q and R. If QR = 12 cm, calculate PQ. (HOTS) (Marks: 5)
Hint: Draw OL ⊥ PS

Answer 1

Answer:

Given OP = 17 cm and OR = OQ = 10 cm

QR = 12 cm (We have interpreted R=12 cm as QR=12cm)

To find PQ:

Drop OM perpendicular to QR.

Since perpendicular from center to chord bisects the chord

MQ = 6 cm

In triangle OMQ, MQ = 6 cm, OQ = 10cm

Using Pythagoras theorem

OM = square root (100 – 36)

= square root (64)

= 8

In triangle OMP, OM = 8 cm, OP = 17 cm

using Pythagoras theorem

PM = square root (289 – 64)

= square root (225)

= 15 cm

Clearly PQ = PM – QM

= 15 cm – 6 cm

= 9 cm