A chord of a circle is equal to its radius. Find the angle subtended by this chord at a point in major segment.
Solution:
Given, AB is a chord of a circle
AB is equal to the radius of the circle.
So, AB = BO ------------------------- (1)
Join OA, AC and BC.
Radius of circle = OA = OB
So, OA = OB = AB
Considering triangle OAB,
OAB is an equilateral triangle
We know that each angle of an equilateral triangle is equal to 60 degrees.
So, ∠AOB = 60º
We know that in a circle the angle subtended by an arc at the centre is twice the angle subtended by it at the remaining part of the circle.
So, ∠AOB = 2∠ACB
∠ACB = 1/2 ∠AOB
∠ACB = 60º/2
∠ACB = 30º
Therefore, the angle subtended by the chord AB at a point in major segment is 60º
✦ Try This: In the figure, O is the center of the circle and ACB is a minor arc, then ∠ACB is
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 10
NCERT Exemplar Class 9 Maths Exercise 10.3 Problem 14
A chord of a circle is equal to its radius. Find the angle subtended by this chord at a point in major segment.
Summary:
A chord of a circle is equal to its radius. The angle subtended by this chord at a point in major segment is 60º
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