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The angle subtended by a chord at its centre is 60°, then the ratio between chord and radius is
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- 1 : 2
- 1 : 1
- √2 : 1
- 2 : 1
- 1 : 2
Correct Option: B
On the basis of question we draw a figure of a circle with centre O
OA = OB = r units
∠AOC = 30°; AC = CB
In ∆ AOC,
| sin AOC = | |
| OA |
| ⇒ sin 30° = | |
| r |
| ⇒ | = | ||
| 2 | r |
| ⇒ AC = | |
| 2 |
| ⇒ AB = 2 × | = r units | |
| 2 |
∴ Required ratio = 1 : 1
Second Method to solve this question :
OA = OB
∴ ∠OAB = ∠OBA = 60°
∴ ∆ OAB is an equilateral triangle.
∴ OA = OB = AB
