Angle subtended by a chord PQ on the centre of the circle is 140 degree. What will be the angle subtended by the chord PQ on the major arc of the circle?

Explanation

Given: The angle subtended by a chord on the major arc of a circle is 65 degrees. 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: 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 = 140° Here, ∠POQ is the angle subtended by the same chord, PQ on the centre of the circle. According to the concept, ∠POQ = 2 × ∠PRQ ⇒ ∠PRQ = 140°/2 ⇒ ∠PRQ = 70° ∴ the angle subtended by the chord AB on the major arc of the circle is 7 0°.