AB is a chord of a circle with centre O and P is any point on the circle. If ∠ APB = 122º, then what is the measure of ∠ OAB?

AB is a chord of a circle with centre O and P is any point…

AB is a chord of a circle with centre O and P is any point on the circle. If $\angle$ APB = 122º, then what is the measure of $\angle$ OAB?

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. 32º

APBQ is a cyclic quadrilateral,

$\angle$ APB + $\angle$ AQB = 180

$\angle$ AQB = 180 - 122 = 58

$\angle$ AOB = 2 × 58 = 116°.

Now in triangle AOB,

$\angle$ OAB = (180 - 116)/2 (OA = OB)

$\angle$ OAB = 32°.