NCERT Solutions for Class 9 Maths Chapter 10

Important NCERT Questions

Circles

NCERT Books for Session 2022-2023

CBSE Board, UP Board and Other state Boards

EXERCISE 10.5

Page No:185

Questions No:2

# 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.

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Given : In circle C (O,r), OA = AB.

To find: ∠ADB and ∠ACB.

Solution: In ΔOAB

OA = AB [∵ Given]

OA = OB [∵ Radii of circle]

Hence, OA = OB = AB

⇒ ABC is an equilateral triangle.

Therefore, ∠AOB = 60° [∵ Each angle of an equilateral triangle is 60°]

∠AOB = 2 ∠ADB

[∵ The angle subtended by an arc at the centre is double the angle subtended by it at

any]

⇒ ∠ADB = 1/2 ∠AOB ⇒ ∠ADB = (1/2) × 60° = 30

ACBD is a cyclic quadrilateral.

Therefore, ∠ACB + ∠ADB = 180°

[∵ the sum of either pair of opposite angles of a cyclic quadrilateral is 180°]

⇒ ∠ACB + 30° = 180° [∵ ∠ADB = 30°]

⇒ ∠ACB = 180° – 30° = 150°