In Fig. 10.11, AOC is the diameter of the circle and arc AXB = 1/2 arc BYC. Find ∠BOC.

Solution:

Given, AOC is the diameter of the circle

arc AXB = 1/2 arc BYC

We have to find ∠BOC

Given, arc AXB = 1/2 arc BYC

So, ∠AOB = 1/2 ∠BOC

We know that the linear pair of angles is equal to 180 degrees.

∠AOB + ∠BOC = 180°

1/2 ∠BOC + ∠BOC = 180°

(1 + 2)/2 ∠BOC = 180°

3/2 ∠BOC = 180°

∠BOC = 2/3 (180°)

∠BOC = 2(60°)

Therefore, ∠BOC = 120°

✦ Try This: In the figure given below, O is the centre of the circle. Chord CD is parallel to the diameter AB. If ∠ABC = 35°, then find ∠CED.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 10

NCERT Exemplar Class 9 Maths Exercise 10.3 Sample Problem 1

In Fig. 10.11, AOC is the diameter of the circle and arc AXB = 1/2 arc BYC. Find ∠BOC

Summary:

In Fig. 10.11, AOC is the diameter of the circle and arc AXB = 1/2 arc BYC. ∠BOC = 120°

☛ Related Questions:

• In Fig. 10.12, ∠ABC = 45º, prove that OA ⊥ OC
• If arcs AXB and CYD of a circle are congruent, find the ratio of AB and CD
• If the perpendicular bisector of a chord AB of a circle PXAQBY intersects the circle at P and Q, pro . . . .