A, B and C are three points on a circle such that the angles subtended by the chord AB and AC at the centre O are 110° and 130°, respectively. Then the value of ∠ BAC:
In △ OBA, ∠ O = 110° ∠ OBA = ∠ OAB (OB = OA = radius) ∠ O + ∠ OBA + ∠ OAB = 180° 110 + ∠ OAB + ∠ OAB = 180° 2∠ OAB = 70° ∠ OAB = 35° In △ OAC, ∠ O = 130° ∠ OAC = ∠ OCA (OA = OC = radius) ∠ O + ∠ OAC + ∠ OCA = 180° 130 + ∠ OAC + ∠ OAC = 180° 2∠ OAC = 50° ∠ OAC = 25° Now, ∠ BAC = ∠ OAB + ∠ OAC = 35° + 25° = 60°
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