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I'm Up and Down, and Round and Round — Class 9 MCQs with Answers

Class 9 CBSE Mathematics · Chapter 5

90 practice questions · 30 Easy · 30 Medium · 30 Hard · Updated

Practise the most important Class 9 CBSE Mathematics questions from Chapter 5, "I'm Up and Down, and Round and Round". You get 9 timed quizzes made from 90 NCERT-based MCQs, with answers and explanations. The questions are split into 30 Easy, 30 Medium and 30 Hard. Warm up on the basics, then move on to the exam-level questions that top scorers in CBSE Board exams and the JEE & NEET foundation years get right.

To score well in "I'm Up and Down, and Round and Round", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This helps you stay accurate when time is short, just as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.

Use this chapter for focused revision. Start with the Easy set to check your basics on I'm Up and Down, and Round and Round, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 9 Mathematics mastery score. Try the 6 sample questions below: tap an option to see the answer and a worked explanation. Sign in free to start practising.

I'm Up and Down, and Round and Round — important questions & MCQs with answers (Class 9 Mathematics)

6 solved questions from this chapter's difficulty levels, each with its answer and explanation. Tap an option to check yourself.

  1. Q1Easy

    The longest chord of a circle is called its:

    Show answer

    Answer: diameter

    Explanation: The diameter is a chord that passes through the centre, and among all chords it is the longest — any chord not through the centre is shorter than it, never longer.

  2. Q2Easy

    The perpendicular drawn from the centre of a circle to a chord:

    A circle with centre O and a chord AB. The perpendicular from O meets the chord at M, with a right-angle mark at M.

    Show answer

    Answer: bisects the chord

    Explanation: The perpendicular dropped from the centre to a chord always bisects that chord into two equal halves — a key circle theorem, not something that merely doubles or parallels the chord.

  3. Q3Medium

    The centre of the unique circle through three non-collinear points is the point of intersection of the:

    A triangle ABC whose three corners do not lie on one straight line.

    Show answer

    Answer: perpendicular bisectors of the sides

    Explanation: The centre must be equidistant from all three points, and the set of points equidistant from two of them is the perpendicular bisector of the segment joining them — so the centre lies at their intersection, not at the medians or altitudes.

  4. Q4Medium

    O is the centre of a circle and A, B are on it with ∠AOB = 110°. If C is a point on the major arc AB, then ∠ACB is:

    A circle with centre O. Points A and B lie on the circle with angle AOB marked 110°. A point C on the major arc AB is joined to A and B, and the angle ACB is marked with a question mark.

    Show answer

    Answer: 55°

    Explanation: The angle at the circumference is half the central angle: ∠ACB = 110° ÷ 2 = 55°. Using the full 110° would ignore the halving rule for a point on the major arc.

  5. Q5Hard

    ABCD is a cyclic quadrilateral with centre O and ∠BCD = 120°. The central angle ∠BOD (on the side of C) is:

    A cyclic quadrilateral ABCD drawn inside its circle with centre O. The angle at C is marked 120°. The radii OB and OD are drawn and the angle BOD is marked with a question mark.

    Show answer

    Answer: 120°

    Explanation: ∠BAD = 180° − 120° = 60° (opposite angle); central angle = 2 × inscribed angle, so ∠BOD = 2 × 60° = 120°, not 240° (doubling ∠BCD directly).

  6. Q6Hard

    In a circle of radius 13 cm, two parallel chords of lengths 10 cm and 24 cm lie on opposite sides of the centre. The distance between them is:

    A circle with centre O and radius OP = 13 cm. Two parallel chords AB (24 cm) and CD (10 cm) lie on opposite sides of the centre. The distance between the chords is marked with a question mark.

    Show answer

    Answer: 17 cm

    Explanation: The two chords sit √(13² − 5²) = 12 cm and √(13² − 12²) = 5 cm from the centre; since they are on opposite sides, the distance between them is the sum, 12 + 5 = 17 cm, not the difference 7 cm.

Key concepts: I'm Up and Down, and Round and Round (Class 9 Mathematics)

Everything in a circle follows from one fact: every point on it is the same distance from the centre. From that single property come the chord theorems, the relationship between the angle at the centre and the angle at the circumference, and the rule that opposite angles of a cyclic quadrilateral are supplementary.

Circle
The set of all points at a fixed distance (the radius) from a fixed point (the centre). Every theorem in the chapter is a consequence of this one definition.
Chord
A segment joining two points on the circle. The longest possible chord is the diameter, which passes through the centre.
Arc, sector and segment
An arc is a piece of the circle itself; a sector is the region between two radii and an arc; a segment is the region between a chord and its arc.
A circle with centre O. At the top left, the region between two radii and the arc joining them is shaded green and labelled sector. At the bottom, the region between a chord and the arc below it is shaded amber and labelled segment, with the chord labelled. On the right, a piece of the circle itself is drawn thick and labelled arc.
Perpendicular from centre to a chord
The perpendicular dropped from the centre bisects the chord, and conversely the line from the centre to a chord's midpoint is perpendicular to it.
A circle with centre O and a chord AB below the centre. The perpendicular from O meets the chord at M, with a right-angle mark at M. The two halves AM and MB carry equal tick marks: the perpendicular from the centre bisects the chord.
Equal chords are equidistant
Chords of equal length lie the same distance from the centre, and chords equidistant from the centre are equal. Longer chords sit closer to the centre.
A circle with centre O and two chords of equal length, AB at the bottom and CD at the upper right, each marked with a single tick. Perpendiculars from O meet them at M and N, with right-angle marks, and the distances OM and ON carry equal double ticks: equal chords are the same distance from the centre.
Angle subtended at the centre
The angle a chord or arc makes at the centre. Equal chords subtend equal angles at the centre, and equal central angles cut off equal chords.
Angle at centre is twice angle at circumference
An arc subtends at the centre an angle exactly double the angle it subtends anywhere on the remaining part of the circle.
A circle with centre O. The arc AB at the bottom is drawn thick in amber. It subtends the angle AOB at the centre, marked 2x, and the angle APB at a point P on the remaining part of the circle, marked x.
Angles in the same segment
All angles subtended by the same arc at points on the same side of it are equal, since each is half the same central angle.
A circle with a chord AB near the bottom. Two points P and Q lie on the circle on the same side of AB, the upper part. The angles APB and AQB, both standing on the arc AB, are each marked x: they are equal.
Angle in a semicircle
An angle subtended by a diameter at any point of the circle is a right angle — the central angle is 180°, so the inscribed angle is 90°.
A circle with centre O and a diameter AB through the centre. A point P on the circle is joined to A and B; the angle APB at P is marked as a right angle.
Cyclic quadrilateral
A quadrilateral with all four vertices on one circle. Its opposite angles are supplementary, adding to 180°.
A quadrilateral ABCD with all four vertices on a circle. The angle at A is marked x and the opposite angle at C is marked 180° − x; the angle at B is marked y and the opposite angle at D is marked 180° − y. Opposite angles add to 180°.
Converse for cyclic quadrilaterals
If one pair of opposite angles of a quadrilateral adds to 180°, the four vertices must lie on a circle — the standard test for concyclic points.
Exterior angle of a cyclic quadrilateral
The exterior angle at any vertex equals the interior opposite angle, which follows directly from the supplementary-angles property.
Concyclic points
Points that all lie on one circle. Showing that a segment subtends equal angles at two points on the same side proves they are concyclic.
Circumcentre
The centre of the circle through all three vertices of a triangle, found where the perpendicular bisectors of the sides meet.
A triangle ABC with the circle through its three vertices. The perpendicular bisector of each side is drawn dashed, with a right-angle mark where it crosses the side at its midpoint. The three bisectors meet at one point O, the circumcentre, which is the centre of the circle.
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I'm Up and Down, and Round and Round — FAQs

What are the key concepts in Class 9 Mathematics I'm Up and Down, and Round and Round?+

Everything in a circle follows from one fact: every point on it is the same distance from the centre. From that single property come the chord theorems, the relationship between the angle at the centre and the angle at the circumference, and the rule that opposite angles of a cyclic quadrilateral are supplementary. Key ideas include Circle, Chord, Arc, sector and segment, Perpendicular from centre to a chord, Equal chords are equidistant, Angle subtended at the centre.

What does Class 9 Mathematics Chapter 5 (I'm Up and Down, and Round and Round) cover on XamBaaz?+

It has 90 NCERT-based MCQs on "I'm Up and Down, and Round and Round": 30 Easy, 30 Medium and 30 Hard. Together they make 9 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE Board exams and the JEE & NEET foundation years.

Are these "I'm Up and Down, and Round and Round" questions free to practise?+

Yes. Sign in with Google to practise "I'm Up and Down, and Round and Round" free. Full unlimited access is ₹999/year. One year from the day you pay. You stay in Class 9 till 31 March; on 1 April your account moves up to Class 10 and the rest of your year carries over. No chapter is charged separately.

How should I revise "I'm Up and Down, and Round and Round" for the exam?+

Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 9 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.

Are these "I'm Up and Down, and Round and Round" MCQs available with answers?+

Yes. 6 sample questions are on this page with answers: tap an option, or "Show answer", to see the correct option and a step-by-step explanation. Sign in free with Google to start practising, with instant scoring.

Is there negative marking in the "I'm Up and Down, and Round and Round" quizzes?+

Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.

What are the important questions from I'm Up and Down, and Round and Round (Class 9 Mathematics)?+

The questions that matter most test Circle, Chord, Arc, sector and segment, Perpendicular from centre to a chord, Equal chords are equidistant, Angle subtended at the centre. This page shows 6 solved important MCQs with answers and explanations. Sign in to practise all 90 questions on the chapter as timed quizzes.

Is there an online quiz for I'm Up and Down, and Round and Round?+

Yes — Class 9 Mathematics I'm Up and Down, and Round and Round has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.

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