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

Quantitative Aptitude ( CCS) Geometry

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

2:1

1:1

1:2

5:3

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Explanation:

∠AOB = 60°
OA = OB = r (radii)
∴ ∠ABO = ∠OAB
In ΔAOB,
∠AOB + ∠OAB + ∠ABO = 180°
60° + 2∠OAB = 180° [? ∠OAB = ∠ABO]
2∠OAB = 180° – 60° = 120°
∠OAB = 60° = ∠ABO
ΔAOB is an equilateral triangle.
∴ OA = OB = AB
∴ AB : OA = r : r = 1 : 1