Question

The angle subtended by a chord at its centre is 60°, then the ratio between chord and radius is

पर्याय

• 1 : 2

• 1 : 1

• `sqrt(2) : 1`

• 2 : 1

Answer 1

1 : 1

Explanation:

OA = OB = r units

∠AOC = 30°; AC = CB

In ΔAOC,

sin AOC = `(AC)/(OA)`

⇒ sin 30° = `(AC)/r`

⇒ `1/2 = (AC)/r`

⇒ AC = `r/2`

⇒ AB = `2 xx r/2` = r units

∴ Required ratio = 1 : 1

Second Method

OA = OB

∴ ∠OAB = ∠OBA = 60°

∴ ΔOAB is an equilateral triangle

∴ OA = OB = AB