Assertion Reason Questions For Class 9 Maths Chapter 5 Im Up And Down And Round And Round

Assertion and Reason questions for Class 9 Maths Chapter 5, I’m Up and Down, and Round and Round, are available in this Maths article. These questions are very helpful for understanding the chapter and solving geometry-based problems with ease. Our subject experts have provided detailed solutions based on the CBSE syllabus and the NCERT textbook. This study material helps students build conceptual clarity, practise important question types, and prepare well for examinations. A free downloadable PDF is also available for quick revision and practice.

Assertion and Reason Questions on Class 9 Maths Chapter 5: I’m Up and Down, and Round and Round

Directions: In each question below, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:

(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.

Question 1
Assertion: A circle can be drawn through any three points on a plane.
Reason: Three non-collinear points determine a unique circle.
Answer: (D)
Explanation: The assertion is not always true, because if the three points lie on one straight line, no circle can pass through them. The reason is true, but only for non-collinear points.

Question 2
Assertion: The centre of the circumcircle of an acute-angled triangle lies inside the triangle.
Reason: The perpendicular bisectors of the sides of an acute triangle meet at a point inside it.
Answer: (A)
Explanation: Both statements are true, and the reason correctly explains the assertion. In an acute triangle, the circumcentre lies inside the triangle.

Question 3
Assertion: A chord passing through the centre of a circle is the longest chord of that circle.
Reason: A chord through the centre is called the diameter.
Answer: (A)
Explanation: Both statements are true. A diameter is the longest chord because it passes through the centre and has length equal to twice the radius.

Question 4
Assertion: Equal chords of a circle subtend equal angles at the centre.
Reason: Equal chords are at equal distances from the centre.
Answer: (A)
Explanation: Both statements are true, and the reason supports the assertion. Equal chords subtend equal angles and are also equally distant from the centre.

Question 5
Assertion: The line joining the centre of a circle to the midpoint of a chord is perpendicular to the chord.
Reason: The line from the centre to the midpoint of a chord divides the chord into two equal parts.
Answer: (B)
Explanation: Both statements are true, but the reason is not the complete explanation. The actual proof uses the congruence of the two triangles formed on either side of the chord.

Question 6
Assertion: Chords that are at equal distance from the centre of a circle are equal in length.
Reason: The perpendicular from the centre to a chord bisects it.
Answer: (B)
Explanation: Both are true, but the reason alone does not fully explain why equal distances from the centre make the chords equal.

Question 7
Assertion: A longer chord lies closer to the centre of the circle.
Reason: The distance of a chord from the centre increases as the chord becomes longer.
Answer: (C)
Explanation: The assertion is true, but the reason is false. In fact, the longer the chord, the nearer it is to the centre.

Question 8
Assertion: The angle subtended by a diameter at any point on the circle is a right angle.
Reason: The angle subtended by an arc at the centre is twice the angle subtended at any point on the remaining part of the circle.
Answer: (A)
Explanation: Both statements are true. Since a diameter subtends 180 degrees at the centre, the angle at the circle is 90 degrees.

Question 9
Assertion: If a line segment subtends equal angles at two points on the same side of it, then those four points are concyclic.
Reason: Equal angles standing on the same chord imply that the points lie on one circle.
Answer: (A)
Explanation: Both statements are true, and the reason correctly explains the assertion. This is the standard test for concyclicity.

Question 10
Assertion: In a cyclic quadrilateral, opposite angles add up to 180 degrees.
Reason: Each opposite angle is half of a full turn at the centre.
Answer: (B)
Explanation: The assertion is true, but the reason is not the proper explanation. The result follows from the angles subtended by arcs, not simply from “half of a full turn.”

Question 11
Assertion: A circle has exactly one line of symmetry.
Reason: Every diameter of a circle is a line of reflection symmetry.
Answer: (C)
Explanation: The assertion is false because a circle has infinitely many lines of symmetry. The reason is true.

Question 12
Assertion: Infinitely many circles can pass through two given points.
Reason: The centres of all such circles lie on the perpendicular bisector of the segment joining the two points.
Answer: (A)
Explanation: Both statements are true. Since there are infinitely many points on the perpendicular bisector, there are infinitely many possible centres, so infinitely many circles can be drawn.

Question 13
Assertion: If two chords of a circle are equal, then they are equidistant from the centre.
Reason: Equal chords subtend equal angles at the centre.
Answer: (A)
Explanation: Both are true. Equal chords subtend equal central angles, and that leads to equal distances from the centre.

Question 14
Assertion: The chord nearest to the centre is the longest chord of the circle.
Reason: The diameter is the greatest chord in a circle.
Answer: (C)
Explanation: The assertion is true because the chord closest to the centre is the diameter. The reason is true, but it does not fully explain the assertion in a direct way.

Question 15
Assertion: If two opposite angles of a quadrilateral add up to 180 degrees, then the quadrilateral is cyclic.
Reason: A quadrilateral with supplementary opposite angles can be inscribed in a circle.
Answer: (A)
Explanation: Both statements are true, and the reason correctly explains the assertion. This is the converse of the cyclic quadrilateral theorem.

Download the free PDF of Assertion and Reason Questions on Chapter 5: I’m Up and Down, and Round and Round for Class 9 here for quick revision and practice.

Download the PDF: Assertion and Reason Questions on Chapter 5: I’m Up and Down, and Round and Round for Class 9