# Chord AB subtends ∠AOB = 60° at centre. If OA = 5 cm then find the length of AB (in cm).

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by pravin3103

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2014-12-28T11:23:28+05:30

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∠AOB = 60°
OA =radius = 5 cm
OB = 5 cm

Since OA=OB, it is a isosceles triangle.
∠ABO = ∠BAO

In the triangle,
∠AOB +∠ABO + ∠BAO = 180°
So ∠ABO + ∠BAO = 180-60 = 120
∠ABO = 120/2 = 60 and
∠BAO = 60

SO it is an equilateral triangle. So all sides are equal.
Hence AB = 5cm
2014-12-28T14:47:00+05:30
Let the triangle be AOB where ∠AOB = 60°
Then we have AO = BO = 5 cm
Since Δ AOB is a isosceles triangle.
∠ABO = ∠BAO = (180-60)/2 = 60  degree
Hence we have, ΔAOB is an equiangular triangle hence an equilateral triangle where all sides are equal ⇒ AO = BO = AB = 5 cm
Length of AB is 5 cm