In the figure O is the centre of the circle A and B are points on the circle. LAOB=60° and AB=6 centimetres. What is the length of radius of circle in centimetres ? A. 3 B. 6 C. 10 D. 12
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Fig. 1, 'O' is the centre of a circle and OBA = 60^∘ . Then ACB equals
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B. 6
Step-by-step explanation:
In Δ AOB
AB = 6 cm (∵ Given)
∠ AOB = 60° (∵ Given)
AO = OB (∵ Radii of same circle)
∴ ∠OAB = ∠OBA (∵ Base angles of isosceles triangle)
let ∠OAB & ∠OBA be x
∠AOB + x + x = 180°
∠AOB + 2x = 180°
60° + 2x = 180 ° (∵ ∠AOB = 60°)
2x = 180° - 60°
2x = 120°
x = 60°
∴ ∠AOB = ∠OBA = ∠OAB = 60°
Hence triangle is equilateral triangle.
∴ AB = OA = OB = 6
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