A B and C are the three points on a circle such that the angles subtended by the chords AB and AC at...........

Quantitative Aptitude ( CCS) Geometry

A, B and C are the three points on a circle such that the angles subtended by the chords AB and AC at the centre O are 90° and 110° respectively. ∠BAC is equal to

170°

70°

90°

80°

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Explanation:

We know that,
∠BOA + ∠AOC + ∠BOC = 360°
90° + 110° + ∠BOC = 360°
∠BOC = 360° – 200° = 160°
Note : The angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.
∴ ∠BAC = 1/2∠BOC = 1/2× 160° = 80°