In Fig. 10.36, A, B and C are three points on a circle with centre O such that ∠BOC = 30º and ∠AOB = 60º. If D is a point on the circle other than the arc ABC, find ∠ADC.

Solution:

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

∠AOC = ∠AOB + ∠BOC = 90°

∠AOC = 2 ∠ADC (By Theorem 10.8)

∠ADC = 1/2 ∠AOC

∠ADC = 1/2 × 90 = 45°

∴ ∠ADC = 45°

☛ Check: NCERT Solutions for Class 9 Maths Chapter 10

Video Solution:

In Fig. 10.36, A, B and C are three points on a circle with center O such that ∠BOC = 30º and ∠AOB = 60º. If D is a point on the circle other than the arc ABC, find ∠ADC.

Maths NCERT Solutions Class 9 Chapter 10 Exercise 10.5 Question 1

Summary:

If, in the given figure, A, B, and C are three points on a circle with center O such that ∠BOC = 30° and ∠AOB = 60°, D is a point on the circle other than the arc ABC, then ∠ADC = 45°.

☛ Related Questions:

• A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc.
• In Fig. 10.37, ∠PQR = 100° where P, Q and R are points on a circle with center O. Find ∠OPR.
• In Fig. 10.38, ∠ABC = 69° and ∠ACB= 31°, find ∠BDC.
• In Fig. 10.39, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠BEC = 130° and ∠ECD = 20°. Find ∠BAC.