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Question
In the given figure, 5 × PA = 3 × AB = 30 cm and PC = 4 cm. Find CD.
Solution
Since two chords AB and CD intersect each other at P.
∴ AP × PB = CP × PD
But 5 × PA = 3 × AB = 30 cm
∴ 5 × PA = 30 cm `=>` PA = 6 cm
And 3 × AB = 30 cm `=>` AB = 10 cm
`=>` BP = PA + AB
= 6 + 10
= 16 cm
Now,
AP × PB = CP × PD
`=>` 6 × 16 = 4 × PD
`=>` PD = `(6 xx 16)/4` = 24 cm
CD = PD – PC
= 24 – 4
= 20 cm
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