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Question
An equilateral triangle ABC is inscribed in a circle with centre O. The measures of ∠BOCis
Options
30°
60°
90°
120°
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Solution
120°
We are given that an equilateral ΔABC is inscribed in a circle with centre O. We need to find ∠BOC
We have the following corresponding figure:
We are given AB = BC = AC
Since the sides AB, BC, and AC are these equal chords of the circle.
So, the angle subtended by these chords at the centre will be equal.
Hence
`angleAOB + angleBOC + angleAOC = 360`
`angleBOC + angleBOC + angleBOC = 360`
`3angleBOC = 360`
`angleBOC = 360/3`
`angleBOC = 120°`
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