Points A and B are on circle with centre O, PAM and PBN…

Points A and B are on circle with centre O, PAM and PBN are tangents to the circle at A and B respectively from a point P outside the circle. Point Q is on the major are AB such that ∠QAM = 58° and ∠QBN = 50°, then find the measure (in degree) of ∠APB.

Show answer & explanation

Correct answer: A

Explanation

The correct answer is Option 1. i.e 36.

One knows that the radius is always perpendicular to the tangent.

$\angle$ QAM = 58° so $\angle$ OAQ = 90 - 58 = 32°.

$\angle$ QBN = 50° so $\angle$ OBQ = 90 - 50 = 40°.

OA = OQ = OB = Radius

$\angle$ OAQ = $\angle$ OQA = 32° and $\angle$ OBQ = $\angle$ OQB = 40°

$\angle$ AQB = 32 + 40 = 72°.

(Angle subtended by the arc at the centre is twice of the angle subtended by the same arc at any point of the circumference)

$\angle$ AOB = 2 × 72 = 144.

$\angle$ APB = 180 - $\angle$ AOB = 180 - 144 = 36°.

SSC CGL 2021 PYQ — Question 73