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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.

Byju's Answer Standard IX Mathematics Chord A chord of a ... Question Question 14

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

Open in App Solution

Given, AB is a chord of a circle, which is equal to the radius of the circle, i.e., AB = BO

Join OA, AC and BC.

Since OA = OB = radius of circle i.e.,AB = OA=OB

Thus, Δ O A B

is an equilateral triangle.

⇒ ∠ A O B = 60 ∘

[each angle of an equilateral triangle is

60 ∘ ]

By using the theorem, 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.

i . e . , ∠ A O B = 2 ∠ A C B ∠ A C B = 60 ∘ 2 = 30 ∘

The angle subtended by the chord AB at a point in the major segment is

30 ∘ . Suggest Corrections 16

SIMILAR QUESTIONS

Q. A chord of a circle is equal to its radius Find the angles subtended by this chord at a point in major segmentQ. A chord of a circle is equal to its radius. The angle subtended by this chord at a point in major segment isQ. Fill In The Blanks

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

Q.

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 major arc.

Q. Question 2

A chord AB of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the major arc and also at a point on the minor arc.

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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 - A chord of a circle is equal to its radius. The angle subtended by this chord at a point

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 10NCERT 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

☛ Related Questions:

In Fig.10.13, ∠ADC = 130° and chord BC = chord BE. Find ∠CBE

In Fig.10.14, ∠ACB = 40º. Find ∠OAB

A quadrilateral ABCD is inscribed in a circle such that AB is a diameter and ∠ADC = 130º. Find ∠BAC

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The length of a chord of a circle is equal to the radius of the circle. The angle which this chord subtends on the longer segment of the circle is equal to

Click here👆to get an answer to your question ✍️ The length of a chord of a circle is equal to the radius of the circle. The angle which this chord subtends on the longer segment of the circle is equal to

Question

The length of a chord of a circle is equal to the radius of the circle. The angle which this chord subtends on the longer segment of the circle is equal to

A30

o

B45

o

C60

o

D90

o Medium Open in App Solution Verified by Toppr

Correct option is A)

Step -1: Finding angle subtended by the chord at the centre

Let AB be the chord of length equal to radius of circle.

∴From the figure given below, AB=OA=OB   (∵OA, OB = radius of circle)

In △AOB,

△AOB is an equilateral triangle.

∴∠AOB=∠OAB=∠OBA=60 ∘

(∵Angles of an equilateral triangle = 60

∘ )

Step -2: Finding angle subtended by the chord over major segment.

We know, ∠AOB=2×∠ACB

∠ACB= 2 1 ​ ×∠AOB ∠ACB= 2 1 ​ ×60 ∘ ∠ACB=30 ∘

Hence, the angle subtended by the chord on the major segment is equal to 30

∘ .

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