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. The value of ∠BAC is:

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SSC CGL Previous Paper 65 (Held On: 3 March 2020 Shift 1)
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  1. 75°
  2. 70°
  3. 60°
  4. 65°

Answer (Detailed Solution Below)

Option 3 : 60°
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F1 Ashish 07-04-2020 Savita ..D1

from the following figure.

∠AOB = 110° and ∠AOC = 130°

As we know,

∠AOB + ∠AOC + ∠BOC = 360°

∠BOC = 360° - 110° - 130° = 120°

∠BAC = ∠BOC/2

∴ ∠BAC = 120°/2 = 60°

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