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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 : Two diameters of a circle intersect each other at right angles. Then the quadrilateral formed by joining their end-points is a square.
Reason : Equal chords 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 'A'. Can you explain this answer?
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Verified Answer
Direction: In the following questions, a statement of Assertion is gi...
Let AB and CD be two perpendicular diameters of a circle with centre O.
Now, ∠ABC = 90º
[Angle in semicircle is a right angle]
Similarly ∠ACD = ∠ADC
= ∠BAD = 90º ...(1)
In ΔAOB and ΔAOD, we have
AO = AO (Common)
∠AOB = ∠AOD (Each 90º, given)
BO = OD (Radii of circle)
ΔAOB ≅ ∠AOD(By SAS congruence)
AB = AD (By C.P.C.T.)
Similarly, we have,
AD = DC , DC = BC; BC = AB
Hence, AB = BC = CD = DA ...(2)
Also, it is given that diagonals of ABCD intersect at
90º ...(3)
By (1), (2) and (3) ABCD is a square.
Most Upvoted Answer
Direction: In the following questions, a statement of Assertion is gi...
Assertion: Two diameters of a circle intersect each other at right angles. Then the quadrilateral formed by joining their end-points is a square.
Reason: Equal chords subtend equal angles at the centre.
Explanation:
To understand the given assertion and reason, let's break down the information provided and analyze it step by step.
1. Two diameters of a circle intersect each other at right angles:
- A diameter is a line segment passing through the center of a circle and having both its endpoints on the circle.
- When two diameters intersect each other, they form four angles at their intersection point, also known as the center of the circle.
- Since the diameters intersect at right angles, the four angles formed are all right angles.
2. The quadrilateral formed by joining their end-points is a square:
- A quadrilateral is a polygon with four sides.
- If the four angles of a quadrilateral are all right angles, then it is a square.
- In this case, the four angles formed at the intersection of the diameters are all right angles, so the quadrilateral formed is a square.
3. Equal chords subtend equal angles at the center:
- A chord is a line segment that connects two points on the circumference of a circle.
- If two chords of a circle are equal in length, then the angles they subtend at the center of the circle are also equal.
- This property is useful in determining the congruence of angles formed by chords in a circle.
Now, let's analyze the relationship between the assertion and the reason:
- The assertion states that when two diameters of a circle intersect at right angles, the quadrilateral formed is a square.
- The reason states that equal chords subtend equal angles at the center.
- In this case, the two diameters of the circle intersect at right angles, forming equal chords.
- Since the equal chords subtend equal angles at the center, the four angles formed at the intersection of the diameters are all equal and right angles.
- Therefore, the reason correctly explains why the quadrilateral formed is a square.
Hence, both the assertion and reason are true, and the reason is the correct explanation of the assertion. Therefore, the correct answer is option A.
Reason: Equal chords subtend equal angles at the centre.
Explanation:
To understand the given assertion and reason, let's break down the information provided and analyze it step by step.
1. Two diameters of a circle intersect each other at right angles:
- A diameter is a line segment passing through the center of a circle and having both its endpoints on the circle.
- When two diameters intersect each other, they form four angles at their intersection point, also known as the center of the circle.
- Since the diameters intersect at right angles, the four angles formed are all right angles.
2. The quadrilateral formed by joining their end-points is a square:
- A quadrilateral is a polygon with four sides.
- If the four angles of a quadrilateral are all right angles, then it is a square.
- In this case, the four angles formed at the intersection of the diameters are all right angles, so the quadrilateral formed is a square.
3. Equal chords subtend equal angles at the center:
- A chord is a line segment that connects two points on the circumference of a circle.
- If two chords of a circle are equal in length, then the angles they subtend at the center of the circle are also equal.
- This property is useful in determining the congruence of angles formed by chords in a circle.
Now, let's analyze the relationship between the assertion and the reason:
- The assertion states that when two diameters of a circle intersect at right angles, the quadrilateral formed is a square.
- The reason states that equal chords subtend equal angles at the center.
- In this case, the two diameters of the circle intersect at right angles, forming equal chords.
- Since the equal chords subtend equal angles at the center, the four angles formed at the intersection of the diameters are all equal and right angles.
- Therefore, the reason correctly explains why the quadrilateral formed is a square.
Hence, both the assertion and reason are true, and the reason is the correct explanation of the assertion. Therefore, the correct answer is option A.
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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 : Two diameters of a circle intersect each other at right angles. Then the quadrilateral formed by joining their end-points is a square.Reason : Equal chords 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 'A'. 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 : Two diameters of a circle intersect each other at right angles. Then the quadrilateral formed by joining their end-points is a square.Reason : Equal chords 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 'A'. 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 : Two diameters of a circle intersect each other at right angles. Then the quadrilateral formed by joining their end-points is a square.Reason : Equal chords 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 'A'. 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 : Two diameters of a circle intersect each other at right angles. Then the quadrilateral formed by joining their end-points is a square.Reason : Equal chords 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 'A'. 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 : Two diameters of a circle intersect each other at right angles. Then the quadrilateral formed by joining their end-points is a square.Reason : Equal chords 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 'A'. 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 : Two diameters of a circle intersect each other at right angles. Then the quadrilateral formed by joining their end-points is a square.Reason : Equal chords 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 'A'. 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 : Two diameters of a circle intersect each other at right angles. Then the quadrilateral formed by joining their end-points is a square.Reason : Equal chords 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 'A'. 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 : Two diameters of a circle intersect each other at right angles. Then the quadrilateral formed by joining their end-points is a square.Reason : Equal chords 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 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 9.
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