Q11 of 141 Page 464

In the given figure, AOC is a diameter of a circle with centre O and arc arc BYC. Find ∠BOC.

Given: arc


Here,


2×AXB = BYC


∴ 2×∠AOB = ∠BOC


∠AOB = ∠BOC –1


Here,


∠AOC = ∠AOB + ∠BOC = 180°


∠BOC + ∠BOC = 180° (from –1)


∠BOC = 180°


∠BOC = ×180° = 120°


∴


More from this chapter

All 141 →
9

Prove that a diameter is the largest chord in a circle.

 10

A circle with centre O is given in which ∠OBA = 30° and ∠OCA = 40°. Find ∠BOC.

 12

In the given figure, O is the centre of a circle and ∠ABC = 45°. Prove that OA ⊥ OC.

 13

In the given figure, O is the centre of a circle, ∠ADC = 130° and chord BC = chord BE. Find ∠CBE.