In Fig.10.4, if ∠ABC = 20º, then ∠AOC is equal to:
a. 20º
b. 40º
c. 60º
d. 10º

Solution:

We know that

Angle at the centre of the circle is twice the angle at the circumference subtended by the same arc.

∠AOC = 2 ∠ABC

It is given that

∠ABC = 20º

Substituting the values

∠AOC = 2 × 20º

∠AOC = 40º

Therefore, ∠AOC is equal to 40º.

✦ Try This: If ∠PQR = 40º, then ∠POR is equal to:

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

NCERT Exemplar Class 9 Maths Exercise 10.1 Problem 4

In Fig.10.4, if ∠ABC = 20º, then ∠AOC is equal to: a. 20º, b. 40º, c. 60º, d. 10º

Summary:

Chords equidistant from the centre of a circle are equal in length. In Fig.10.4, if ∠ABC = 20º, then ∠AOC is equal to 40º

☛ Related Questions:

• In Fig.10.5, if AOB is a diameter of the circle and AC = BC, then ∠CAB is equal to: a. 30º, b. 60º, . . . .
• In Fig. 10.6, if ∠OAB = 40º, then ∠ACB is equal to : a. 50º, b. 40º, c. 60º, d. 70°
• In Fig. 10.7, if ∠DAB = 60º, ∠ABD = 50º, then ∠ACB is equal to: a. 60º, b. 50º, c. 70º, d. 80º