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  • A chord of a circle is equal to its radius. Find the angle subtended by this chord at a point in major segment

A chord of a circle is equal to its radius. Find the angle subtended by this chord at a point in major segment

Answers (1)

30o

Solution:

Given that a chord of a circle is equal to its radius

Let the chord be AB as shown in the figure.

AB = Radius of Circle.

Now, AB = OA = OB

In \triangleOAB,

AB = OA = OB = radius

Hence it is an equilateral triangle. So all angles are 60o

\angleOAB =\angleABO = \angleBOA = 60o

Let point D be a point on the major arc.

Considering the arc AB, we know that angle subtended at the centre by an arc is twice the angle subtended by it at any part of the circle

So,

\angle ADB = \frac{1}{2} \angle AOB = \frac{1}{2} (60^{\circ}) = 30^{\circ}

Posted by

infoexpert24

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