AB and BC are two chards of a circie with centre O. Both chords are on either side of the centre O. Point A and point C are connected to the centre O, such that BAO=36° and BCO=40°. What is the degree measure of the angle subtended by the minor arc AC at the centre O?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 168°.
∠BAO = 36° and ∠BCO = 48°
AO, BO, and CO are the radii of the circle.
∠OAB = ∠OBA = 36° (Angles opposite to equal sides are equal)
⇒ ∠OCB = ∠OBC = 48°
⇒ ∠ABC = ∠OBC + ∠OBA = 48° + 36° = 84°
The angle subtended on the circle's center is twice that of the angle subtended by the same arc on the circumference.
The angle subtended by the minor arc AC at the centre O = ∠AOC = 2∠ABC
⇒ ∠AOC = 2 × 84° = 168°
Therefore, the measure of the angle subtended by the minor arc AC at the centre O is 168°.