Two chords AB and PQ of a circle intersect at D inside a

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Two chords AB and PQ of a circle intersect at D inside a circle. If AD = 4 cm., DB = 6 cm., QD = 3 cm., the length of PQ is equal to

1. 11 cm.
2. 8 cm.
3. 9 cm.
4. 10 cm.

Correct Option: A

According to question , we draw a figure of a circle with centre O ,

Here , AD = 4 cm., DB = 6 cm., QD = 3 cm
As we know that , AD × DB = PD × DQ
⇒ 4 × 6 = PD × 3

⇒ PD =	4 × 6	= 8 cm.
	3

∴ PQ = PD + DQ = (8 + 3) cm. = 11 cm.