Chords AB and CD of a circle intersect externally at P.

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Chords AB and CD of a circle intersect externally at P. If AB = 6 cm, CD = 3 cm and PD = 5 cm, then the length of PB is

1. 5 cm
2. 7.35 cm
3. 6 cm
4. 4 cm

Correct Option: B

According to question , we draw a figure of a circle with two chords AB and CD ,

Given , AB = 6 cm; CD = 3 cm
PD = 5 cm; PB = ?
We know that , PA × PB = PC × PD
⇒ (PB – 6) PB = 2 × 5
⇒ PB² – 6PB – 10 = 0

⇒ PB =	6 ± √36 + 40
	2

PB =	6 ± √76	=	6 + 8.7	= 7.35 cm
	2		2