CBSE Class 9 Maths Chapter 5: I’m Up and Down, and Round and Round — Assertion & Reason
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The following Assertion and Reason questions are based on Chapter 5: I'm Up and Down, and Round and Round from the NCERT Class 9 Mathematics textbook. Each question has four options - read both the Assertion (A) and Reason (R) carefully before selecting your answer.
How to attempt Assertion & Reason questions:
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is NOT the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is NOT the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Assertion & Reason Questions
1
Assertion (A): A circle is the locus of points in a plane at a fixed distance from a fixed point.
Reason (R): The fixed point is its centre and the fixed distance is its radius.
Reason (R): The fixed point is its centre and the fixed distance is its radius.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. These two fixed elements define the complete set of points on the circle.
2
Assertion (A): A diameter is the longest chord of a circle.
Reason (R): Every diameter is a line of reflection symmetry of the circle.
Reason (R): Every diameter is a line of reflection symmetry of the circle.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both statements are true, but reflection symmetry does not explain why the chord through the centre has maximum length.
3
Assertion (A): A circle has rotational symmetry through every angle about its centre.
Reason (R): A circle looks unchanged only after rotations of 180 degrees.
Reason (R): A circle looks unchanged only after rotations of 180 degrees.
Answer: (c)
A is true, but R is false. Unlike a polygon with finitely many rotational symmetries, a circle is unchanged by any rotation about its centre.
4
Assertion (A): Every chord of a circle must pass through its centre.
Reason (R): A chord that passes through the centre is called a diameter.
Reason (R): A chord that passes through the centre is called a diameter.
Answer: (d)
A is false, but R is true. Most chords do not pass through the centre; the diameter is the special case that does.
5
Assertion (A): Three non-collinear points determine a unique circle.
Reason (R): The perpendicular bisectors of the sides of their triangle meet at the unique circumcentre.
Reason (R): The perpendicular bisectors of the sides of their triangle meet at the unique circumcentre.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The common intersection is equidistant from all three points and therefore serves as the circle's centre.
6
Assertion (A): Infinitely many circles can pass through two distinct points.
Reason (R): A circle has rotational symmetry about its centre through any angle.
Reason (R): A circle has rotational symmetry about its centre through any angle.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both statements are true, but rotational symmetry does not explain the family of possible circles through the points.
7
Assertion (A): The circumcentre of any triangle is the intersection of its perpendicular bisectors.
Reason (R): The circumcentre must always lie inside the triangle.
Reason (R): The circumcentre must always lie inside the triangle.
Answer: (c)
A is true, but R is false. It lies outside an obtuse triangle and on the hypotenuse of a right triangle.
8
Assertion (A): Three collinear points determine a unique circle.
Reason (R): A unique circle through three points requires the points to be non-collinear.
Reason (R): A unique circle through three points requires the points to be non-collinear.
Answer: (d)
A is false, but R is true. No finite circle can pass through three distinct collinear points.
9
Assertion (A): Equal chords of the same circle subtend equal angles at the centre.
Reason (R): The corresponding triangles formed with the radii are congruent by SSS.
Reason (R): The corresponding triangles formed with the radii are congruent by SSS.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Each triangle has two equal radii and equal chord bases, giving equal included central angles.
10
Assertion (A): If two chords subtend equal angles at the centre, then the chords are equal.
Reason (R): Equal chords of a circle are equidistant from the centre.
Reason (R): Equal chords of a circle are equidistant from the centre.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both results are true, but the equal-distance theorem does not explain the converse relation between central angles and chord lengths.
11
Assertion (A): A line from the centre to the midpoint of a chord is perpendicular to the chord.
Reason (R): Only a diameter can have a midpoint.
Reason (R): Only a diameter can have a midpoint.
Answer: (c)
A is true, but R is false. Every line segment, including every chord, has a midpoint.
12
Assertion (A): A perpendicular drawn from the centre to a chord need not bisect the chord.
Reason (R): A perpendicular from the centre to a chord divides that chord into two equal parts.
Reason (R): A perpendicular from the centre to a chord divides that chord into two equal parts.
Answer: (d)
A is false, but R is true. This bisection is a standard chord theorem.
13
Assertion (A): Equal chords of a circle lie at equal perpendicular distances from the centre.
Reason (R): Congruent right triangles formed by half-chords, radii, and perpendicular distances establish the result.
Reason (R): Congruent right triangles formed by half-chords, radii, and perpendicular distances establish the result.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Equal hypotenuses and corresponding half-chords force the perpendicular distances to be equal.
14
Assertion (A): Of two unequal chords in the same circle, the longer chord is closer to the centre.
Reason (R): A diameter is a chord passing through the centre.
Reason (R): A diameter is a chord passing through the centre.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are correct, but the definition of a diameter does not by itself explain the ordering of distances for all unequal chords.
15
Assertion (A): Chords at equal distances from the centre of the same circle are equal.
Reason (R): Two unequal chords can also be at the same perpendicular distance from the centre.
Reason (R): Two unequal chords can also be at the same perpendicular distance from the centre.
Answer: (c)
A is true, but R is false. The converse chord-distance theorem rules out unequal lengths at the same distance.
16
Assertion (A): The longer of two unequal chords lies farther from the centre.
Reason (R): The longer chord lies closer to the centre.
Reason (R): The longer chord lies closer to the centre.
Answer: (d)
A is false, but R is true. Moving a chord toward the centre increases its length, with the diameter as the longest case.
17
Assertion (A): An arc subtends twice as large an angle at the centre as at a point on the remaining circle.
Reason (R): The central-angle and inscribed-angle theorem relates angles standing on the same arc.
Reason (R): The central-angle and inscribed-angle theorem relates angles standing on the same arc.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The theorem gives central angle = 2 x inscribed angle.
18
Assertion (A): Opposite angles of a cyclic quadrilateral add to 180 degrees.
Reason (R): An angle subtended by a diameter at the circumference is 90 degrees.
Reason (R): An angle subtended by a diameter at the circumference is 90 degrees.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both circle theorems are true, but the semicircle result does not explain every cyclic quadrilateral.
19
Assertion (A): An angle subtended by a diameter at any point on the circle is 90 degrees.
Reason (R): The angle subtended by the same diameter at the centre is 90 degrees.
Reason (R): The angle subtended by the same diameter at the centre is 90 degrees.
Answer: (c)
A is true, but R is false. The diameter forms a straight angle of 180 degrees at the centre, so the inscribed angle is half of it.
20
Assertion (A): Every quadrilateral is cyclic.
Reason (R): A quadrilateral is cyclic if and only if a pair of opposite angles is supplementary.
Reason (R): A quadrilateral is cyclic if and only if a pair of opposite angles is supplementary.
Answer: (d)
A is false, but R is true. Only quadrilaterals satisfying the 180-degree opposite-angle condition can be inscribed in a circle.
❓ Frequently Asked Questions
What is covered in CBSE Class 9 Maths Chapter 5 I’m Up and Down, and Round and Round?
This chapter covers all key topics from I’m Up and Down, and Round and Round as per CBSE 2026-27 syllabus.
Is this Assertion & Reason useful for CBSE board exams?
Yes, designed for CBSE Class 9 board exam preparation covering the complete syllabus.
Are these CBSE Class 9 Maths Assertion & Reason updated for 2026-27?
Yes, all content at eBookPublisher is updated as per the latest 2026-27 CBSE syllabus.
How many chapters are in CBSE Class 9 Maths?
All chapters of CBSE Class 9 Maths are covered at eBookPublisher with free Assertion & Reason for each chapter.
Can I study I’m Up and Down, and Round and Round online for free?
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