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Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer as
Assertion : If A and B are any two points on a circle, then the line segment AB is called a chord of the circle.
Reason : Equal chords of a circle subtend equal angles at the centre.
- a)Both assertion and reason are true and reason is the correct explanation of assertion.
- b)Both assertion and reason are true but reason is not the correct explanation of assertion.
- c)Assertion is true but reason is false.
- d)Assertion is false but reason is true
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Direction: In the following questions, a statement of Assertion is gi...
Given: AB and CD are two equal chords of a circle with a center O.
To Prove: ∠AOB = ∠COD Proof: In Δ AOB and Δ COD,
⇒ OA = OC (Radii of a circle)
⇒ OB = OD (Radii of a circle)
⇒ AB = CD (Given)
Therefore, Δ AOB ≅ Δ COD ( By SSS-criterion of congruence)
By using corresponding parts of congruent triangles
⇒ ∠AOB = ∠COD.
Proved.
Most Upvoted Answer
Direction: In the following questions, a statement of Assertion is gi...
Assertion: If A and B are any two points on a circle, then the line segment AB is called a chord of the circle.
Reason: Equal chords of a circle subtend equal angles at the centre.
The correct answer is option 'B': Both assertion and reason are true but the reason is not the correct explanation of the assertion.
Explanation:
A circle is a closed curve in which all the points on the curve are equidistant from the center. It is composed of infinite points, and any two points on the circle can be connected by a straight line segment. This line segment is called a chord of the circle.
Chords of a Circle:
- A chord is a line segment that connects two points on the circle.
- Chords can be of different lengths depending on the distance between the two points.
- The diameter of a circle is the longest chord, as it passes through the center of the circle.
Angles at the Centre:
- An angle at the center of a circle is formed by two radii (plural of radius) that extend from the center to two points on the circle.
- The measure of an angle at the center is determined by the length of the arc (part of the circumference) that it subtends.
Corresponding Angles and Chords:
- When two chords intersect inside a circle, four angles are formed at the intersection points.
- The angles opposite each other (on the opposite sides of the intersection point) are called vertical angles and are equal.
- However, the angles formed by the intersection of two chords are not necessarily equal to each other.
Counterexample:
To understand why the reason is not the correct explanation of the assertion, consider the following counterexample:
- Take a circle with the center O and two chords AB and CD that subtend equal angles at the center O.
- Now, draw another chord EF that does not pass through the center O.
- Chords EF and CD are equal in length and subtend equal angles at the center O.
- However, chords EF and AB are not equal in length, but they still subtend equal angles at the center O.
- This counterexample shows that equal chords do not necessarily subtend equal angles at the center.
Hence, the reason given is not the correct explanation of the assertion. Both the assertion and reason are true, but they are not directly related to each other.
Reason: Equal chords of a circle subtend equal angles at the centre.
The correct answer is option 'B': Both assertion and reason are true but the reason is not the correct explanation of the assertion.
Explanation:
A circle is a closed curve in which all the points on the curve are equidistant from the center. It is composed of infinite points, and any two points on the circle can be connected by a straight line segment. This line segment is called a chord of the circle.
Chords of a Circle:
- A chord is a line segment that connects two points on the circle.
- Chords can be of different lengths depending on the distance between the two points.
- The diameter of a circle is the longest chord, as it passes through the center of the circle.
Angles at the Centre:
- An angle at the center of a circle is formed by two radii (plural of radius) that extend from the center to two points on the circle.
- The measure of an angle at the center is determined by the length of the arc (part of the circumference) that it subtends.
Corresponding Angles and Chords:
- When two chords intersect inside a circle, four angles are formed at the intersection points.
- The angles opposite each other (on the opposite sides of the intersection point) are called vertical angles and are equal.
- However, the angles formed by the intersection of two chords are not necessarily equal to each other.
Counterexample:
To understand why the reason is not the correct explanation of the assertion, consider the following counterexample:
- Take a circle with the center O and two chords AB and CD that subtend equal angles at the center O.
- Now, draw another chord EF that does not pass through the center O.
- Chords EF and CD are equal in length and subtend equal angles at the center O.
- However, chords EF and AB are not equal in length, but they still subtend equal angles at the center O.
- This counterexample shows that equal chords do not necessarily subtend equal angles at the center.
Hence, the reason given is not the correct explanation of the assertion. Both the assertion and reason are true, but they are not directly related to each other.
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Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : If A and B are any two points on a circle, then the line segment AB is called a chord of the circle.Reason : Equal chords of a circle subtend equal angles at the centre.a)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is trueCorrect answer is option 'B'. Can you explain this answer?
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Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : If A and B are any two points on a circle, then the line segment AB is called a chord of the circle.Reason : Equal chords of a circle subtend equal angles at the centre.a)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is trueCorrect answer is option 'B'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : If A and B are any two points on a circle, then the line segment AB is called a chord of the circle.Reason : Equal chords of a circle subtend equal angles at the centre.a)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is trueCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : If A and B are any two points on a circle, then the line segment AB is called a chord of the circle.Reason : Equal chords of a circle subtend equal angles at the centre.a)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is trueCorrect answer is option 'B'. Can you explain this answer?.
Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : If A and B are any two points on a circle, then the line segment AB is called a chord of the circle.Reason : Equal chords of a circle subtend equal angles at the centre.a)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is trueCorrect answer is option 'B'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : If A and B are any two points on a circle, then the line segment AB is called a chord of the circle.Reason : Equal chords of a circle subtend equal angles at the centre.a)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is trueCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : If A and B are any two points on a circle, then the line segment AB is called a chord of the circle.Reason : Equal chords of a circle subtend equal angles at the centre.a)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is trueCorrect answer is option 'B'. Can you explain this answer?.
Solutions for Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : If A and B are any two points on a circle, then the line segment AB is called a chord of the circle.Reason : Equal chords of a circle subtend equal angles at the centre.a)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is trueCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 9.
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Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : If A and B are any two points on a circle, then the line segment AB is called a chord of the circle.Reason : Equal chords of a circle subtend equal angles at the centre.a)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is trueCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : If A and B are any two points on a circle, then the line segment AB is called a chord of the circle.Reason : Equal chords of a circle subtend equal angles at the centre.a)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is trueCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : If A and B are any two points on a circle, then the line segment AB is called a chord of the circle.Reason : Equal chords of a circle subtend equal angles at the centre.a)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is trueCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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