Question

The figure shows a circle of radius 9 cm with 0 as the centre. The diameter AB produced meets the tangent PQ at P. If PA = 24 cm, find the length of tangent PQ:

Answer 1

Given, Radius of circle (r), OA = OB = 9 cm

Here, PA = 24 cm

Then PB = PA – AB

= 24 – 18

= 6 cm

Then, PB × PA = PQ²   ...(By property)

`\implies` 6 × 24 = PQ²

`\implies` PQ = `sqrt(2 xx 2 xx 2 xx 2 xx 3 xx 3)`

= 2 × 2 × 3

= 12 cm

Hence, the length of tangent PQ is 12 cm.