A, B and C are three points on a circle such that the angles subtended by the chords AB and AC at the centre O are 80o and 120o, respectively. The value of ∠BAC is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e 80o
| Understanding | Application |
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The sum of angles of a triangle is 180°. The measure of the angle in the triangle made by chord except for the one on center is equal. |
In the ∆OAB, ∠O = 80° ⇒ ∠A = ∠B (by the given property) ⇒ ∠A + ∠B = 100° ⇒ ∠A = ∠BAO = 50° In the ∆OAC, ∠O = 120° ⇒ ∠A = ∠C (by the given property) ⇒ ∠A + ∠C = 60° ⇒ ∠A = ∠CAO = 30° ⇒ ∠BAC = ∠BAO + ∠OAC ⇒ ∠BAC = 80° |
