-
Chord PQ is the perpendicular bisector of radius OA of circle with centre O (A is a point on the edge of the circle). If the length of Arc PAQ = 2π/3 . What is the length of chord PQ ?
-
- 2
- √3
- 2√3
- 1
- 2
Correct Option: B
As per the given in question , we draw a figure of a circle with centre O, 
PQ is perpendicular bisector of OA.
∴ OP = OQ = PA = AQ
∴ OPAQ is a rhombus.
As we know that the angle sutended at the centre by an arc is twice to that at the circumference
∴ 2 ∠ PAQ = Reflex ∠POQ
⇒ 2 ∠ PAQ = 360° – ∠POQ
⇒ 3∠ PAQ = 360°
(∵ ∠PAQ = ∠POQ)
| ⇒ ∠PAQ = 120° = ∠POQ = | |
| 3 |
| Again, radius (r) = | = | = 1 | ||
| θ | 2π/3 |
∴ From ∆ OPB
OP = 1 unit
∠POB = 60°
| ∴ sin 60° = | |
| OP |
| ⇒ PB = | |
| 2 |
| ∴ PQ = 2 × | = √3 unit | |
| 2 |
