If a chord of a circle is equal to its radius, then the angle subtended by this chord in major segment isa)45ob)30oc)60od)90oCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Make a circle satisfying above condition
in this figure let o the centre of circle then chord ab=oa=on hence aob is an equilateral triangle so angle aob=60
then angle subtended by the same chord in major segment is half than the angle subtended atcentre
hence acb=30

Answer

Option b

Answer

Answer

The given question asks us to determine the angle subtended by a chord in the major segment of a circle when the chord is equal to the radius of the circle. Let's break down the solution step by step:

1. Angle subtended by a chord in a circle:
- When a chord is drawn in a circle, it creates an arc on the circumference of the circle.
- The angle formed at the center of the circle by the chord is called the angle subtended by the chord.

2. Major segment of a circle:
- In a circle, a major segment is the region between the chord and the circumference of the circle, excluding the minor segment (the region on the other side of the chord).

3. Given information:
- The chord of the circle is equal to its radius. Let's assume the length of the chord and radius to be 'r'.

4. Relationship between the chord and the radius:
- In a circle, if a chord is equal to the radius, it means the chord passes through the center of the circle.
- This implies that the chord is also a diameter of the circle.

5. Diameter and angle subtended:
- A diameter of a circle subtends a right angle (90 degrees) at any point on the circumference of the circle.
- Therefore, when the chord (diameter) is equal to the radius, the angle subtended by the chord is 90 degrees.

6. Options given:
- The options provided are:
a) 45 degrees
b) 30 degrees
c) 60 degrees
d) 90 degrees

7. Correct answer:
- From the above explanation, we conclude that the correct answer is option 'b' - 30 degrees.

In conclusion, when a chord of a circle is equal to its radius, the angle subtended by this chord in the major segment is 30 degrees.

Similar Class 9 Doubts

Rohan draws a circle of radius 10 cm with the help of compass and scale. He also draws two chords, AB and CD in such a way that AB and CD are 6 cm and 8 cm from the centre O. Now, he has some doubts that are given below. Help him out by answering these questions:Q. Which statement is not true?

Let the vertex of an angle ABC be located outside a circle and let the sides of the angles interact equal chord AD and CE with the circle. Prove that angle ABC is equal to half the difference of the angles subtended by the chords AC and DE at the centre.?

To verify that the angle subtended by an arc at the centre of a circle is double the angle subtended at any point on the remaining segment of the circle experimentally.?

The radius of circle is 13cm and the length one of its chords is 10cm then find the distance of the chord from the centre.?

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