PQ is the chord of a circle and O is the center of a circle. ∠POQ = 130 degree. What is the angle subtended by the same chord in the major segment of the circle?

Question

Question

This question was previously asked in

SSC CHSL Tier-I Exam 2022 Official Paper (Held On: 14 March, 2023 Shift 1)

Answer 1

Given:

∠POQ = 130 degree

Concept used:

The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

Calculation:

F1 Vinanti SSC 17.05.23 D1
Let O, R, and PQ be the centre, a point on the major arc, and the aforementioned chord respectively.

So, the major arc for the PQ chord is PRQ.

Hence, ∠POQ = 130 degree

Here, ∠POQ is the angle subtended by the same chord, PQ on the centre of the circle.

According to the concept,

∠POQ = 2 × ∠PRQ

⇒ 130° = 2 ×∠PRQ

⇒ ∠POQ = 65°

∴ The angle subtended by the same chord in the major segment of the circle is 65°.