#### Question

(ii) In the given figure, 5 × PA = 3 × AB = 30 cm and PC = 4cm. 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 = 30cm ⇒ PA = 6cm

And 3× AB =30cm ⇒ AB = 10cm

⇒ BP = PA + AB = 6 + 10 = 16 cm

Now,

AP × PB = CP PD

⇒ 6 × 16 = 4 ×PD

⇒ PD = `(6×16)/4` = 24 cm

CD = PD – PC = 24 – 4 = 20 cm

Is there an error in this question or solution?

Solution (Ii) in the Given Figure, 5 × Pa = 3 × Ab = 30 Cm and Pc = 4cm. Find Cd. Concept: Arc and Chord Properties - If Two Chords Intersect Internally Or Externally Then the Product of the Lengths of the Segments Are Equal.