Two chords of lengths a metre and b metre subtend angles

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Two chords of lengths a metre and b metre subtend angles 60° and 90° at the centre of the circle respectively. Which of the following is true ?

1. b= √2a
2. a = 2√b
3. a = 2b
4. b = 2a

Correct Option: A

As per the given in question , we draw a figure a circle two chords of lengths a metre and b metre subtend angles 60° and 90° at the centre O ,

Radius of circle = r units
In ∆ OCD, ∠COD = 90°
∴ CD² = OC² + OD²
⇒ b² = r² + r² = 2r² ...(i)
In ∆ OAB,
OE ⊥ AB
∠OAB = 60°

AE =	a
	2

∴ cos60° =	AE
	OA

⇒		=	a
	1		2
	2		r

⇒	1	=	a	⇒ a = r........(ii)
	2		2r

From equations (i) and (ii),
b² = 2a²
⇒ b = √2a