Question

In the given figure, 5 × PA = 3 × AB = 30 cm and PC = 4 cm. Find CD.

Answer 1

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