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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:
Solution
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.
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