Question
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:Solution
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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