O midpt 2θ θ ∠AOB = 2∠ACB Semicircle = 90° Opp. cyclic = 180°
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Chapter 9  ·  Class IX Mathematics  ·  MCQ Practice

MCQ Practice Arena

Circles

Chords, Arcs and Cyclic Quadrilaterals — The Most Elegant Theorems in Class IX

📋 50 MCQs ⭐ 28 PYQs ⏱ 75 sec/Q
🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs
16Easy
22Medium
12Hard
28PYQs
75 secAvg Time/Q
8Topics
Easy 32% Medium 44% Hard 24%

Why Practise These MCQs?

CBSE Class IXNTSEState BoardsOlympiad

Circles in Class IX is theorem-rich — equal chords equidistant from centre, angle in a semicircle is 90°, and cyclic quadrilateral properties are CBSE and NTSE staples. CBSE awards a 5-mark proof plus 1–2 MCQs from this chapter. The angle subtended by a chord at the centre is double that at any point on the remaining arc — this theorem and its corollaries produce the most MCQs.

Topic-wise MCQ Breakdown

Circle — Basic Terms & Definitions4 Q
Equal Chords & Equal Distances7 Q
Perpendicular from Centre to Chord7 Q
Angle Subtended by Arc/Chord10 Q
Angle in Semicircle = 90°6 Q
Angles in Same Segment (Equal)7 Q
Cyclic Quadrilateral Properties6 Q
Converse Theorems3 Q

Must-Know Formulae Before You Start

Recall these cold before attempting MCQs — they appear in >70% of questions.

$\text{Equal chords} \Rightarrow \text{equal distances from centre}$
$\text{Perpendicular from centre bisects chord}$
$\angle \text{AOB} = 2\angle\text{ACB}\ (\text{centre vs circumference})$
$\text{Angle in semicircle} = 90°$
$\text{Angles in same segment are equal}$
$\text{Cyclic quad: opp. angles sum} = 180°$
$\text{Exterior angle of cyclic quad = interior opposite angle}$

MCQ Solving Strategy

The most powerful theorem in this chapter: the angle at the centre is DOUBLE the angle at any point on the remaining arc. Use this to derive all other corollaries — semicircle angle (arc = 180° → centre angle = 180° → circumference angle = 90°), same segment angles (equal because they subtend the same arc). For cyclic quadrilateral MCQs, remember opposite angles sum to 180° — use this to find missing angles instantly.

⚠ Common Traps & Errors

Difficulty Ladder

Work through each rung in order — do not jump to Hard before mastering Easy.

① Easy

Basic definitions, perpendicular bisector of chord, angle in semicircle

② Medium

Central vs circumference angle, equal chord distances, cyclic quad angles

③ Hard

Multi-theorem circle problems, converse applications, exterior angle of cyclic quad

★ PYQ

CBSE — prove theorem + numerical angle; NTSE — cyclic quad and chord problems

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 📘✔️ Exercises Step-by-step NCERT solutions ✔️❌ True / False Concept-based True & False ➡ Next Chapter Heron's Formula
🎯 Knowledge Check

Maths — CIRCLES

50 Questions Class 9 MCQs
1
A circle is the collection of all points in a plane that are at a fixed distance from a ______.
2
A line segment joining any two points on a circle is called a ______.
3
The longest chord of a circle is always its ______.
4
The distance from the centre to any point on the circle is called the ______.
5
A semicircle subtends an angle of ______ at the centre.
6
A semicircle subtends an angle of ______ at any point on the circle.
7
If two chords are equal, their corresponding arcs are ______.
8
A region bounded by a chord and its corresponding arc is called a ______.
9
A region bounded by two radii and the included arc is called a ______.
10
If a perpendicular is drawn from the centre to the chord, the chord is ______.
11
If a line from the centre bisects a chord, the line is ______ to the chord.
12
The angle subtended by a chord at the centre is ______ the angle subtended at the remaining part of the circle.
13
A quadrilateral is cyclic if its opposite angles are ______.
14
If all four vertices of a quadrilateral lie on a circle, it is called a ______.
15
In a cyclic quadrilateral, the exterior angle equals the ______ opposite angle.
16
Equal chords of a circle are equidistant from the ______.
17
The perpendicular bisector of any chord passes through the ______.
18
The sum of all angles at the centre around a point is ______.
19
The total number of radii a circle can have is ______.
20
The total number of chords a circle can have is ______.
21
A line intersecting a circle in two points is called a ______.
22
A line touching a circle at exactly one point is called a ______.
23
A circle has exactly ______ line(s) of symmetry.
24
A circle has rotational symmetry of order ______.
25
Angle subtended by diameter at circle is always ______.
26
The number of circles that can pass through 3 non-collinear points is ______.
27
The number of circles that can pass through two given points is ______.
28
Equal arcs subtend ______ angles at the centre.
29
A diameter divides the circle into ______ equal parts.
30
If a chord is moved farther from the centre, its length ______.
31
A circle with centre at origin and radius 5 is represented by points ______ units away.
32
In a circle, the locus of points at constant distance from centre is the ______.
33
In a cyclic quadrilateral, sum of opposite angles is ______.
34
A closed curve having all points at equal distance from centre is called ______.
35
A diameter is a chord that ______ the centre.
36
The boundary of a circle is called the ______.
37
The common point of a tangent and a circle is called ______.
38
The measure of a full circle at centre is ______.
39
The part of the circumference between two points is called a ______.
40
A major arc is ______ than 180°.
41
A minor arc is ______ than 180°.
42
If centre lies inside the quadrilateral, the quadrilateral is ______ cyclic.
43
A radius is a line segment from centre to ______.
44
Equal chords subtend ______ arcs.
45
The degree measure of a semicircle is ______.
46
The entire angle at centre is ______ times the angle at circumference.
47
Which of the following is always cyclic?
48
A quadrilateral whose vertices lie on a circle is called ______.
49
The angle subtended by an arc at the centre depends on the ______.
50
The centre of a circle can be located by drawing ______.
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NCERT Class 9 Circles 50 MCQs with Answers
NCERT Class 9 Circles 50 MCQs with Answers — Complete Notes & Solutions · academia-aeternum.com
Multiple Choice Questions (MCQs) are one of the most effective tools for mastering Chapter 9 “Circles” of NCERT Class 9 Mathematics. This chapter builds a clear understanding of key geometric ideas, including radius, diameter, chords, arcs, central angles, segments, sectors, and important theorems such as perpendicular bisector property, equal chord theorem, angle subtended by a chord, and properties of cyclic quadrilaterals. These MCQs are carefully designed to strengthen conceptual clarity,…
🎓 Class 9 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
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Exam tip: Sharing chapter notes with your study group creates a reinforcement loop. Teaching a concept is the fastest path to mastering it.

Frequently Asked Questions

A circle is a set of all points in a plane that are at a fixed distance (radius) from a fixed point called the centre.

The distance from the centre to any point on the circle. All radii of a circle are equal.

A line segment passing through the centre and touching both ends of the circle. It is twice the radius.

\( \text{Diameter} = 2 \times \text{Radius} \).

A chord is any line segment joining two points on a circle.

The diameter is the longest chord.

A part of the circumference between two points is called an arc.

The smaller arc between two points on a circle.

The larger arc between the same two points on a circle.

A \(180^\circ\) arc formed by endpoints of the diameter.

A region bounded by a chord and its corresponding arc.

Minor segment and major segment.

A region enclosed by two radii and the connecting arc.

The angle subtended at the centre by an arc or chord.

Angle formed at centre by joining centre with chord endpoints.

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    CIRCLES — Learning Resources

    📄 Detailed Notes
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    📌 Exercise
    📝 Exercises
    Exercise-9.1 Exercise-9.2 Exercise-9.3
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    ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025
    Sharing this chapter
    NCERT Class 9 Circles 50 MCQs with Answers
    NCERT Class 9 Circles 50 MCQs with Answers — Complete Notes & Solutions · academia-aeternum.com
    Multiple Choice Questions (MCQs) are one of the most effective tools for mastering Chapter 9 “Circles” of NCERT Class 9 Mathematics. This chapter builds a clear understanding of key geometric ideas, including radius, diameter, chords, arcs, central angles, segments, sectors, and important theorems such as perpendicular bisector property, equal chord theorem, angle subtended by a chord, and properties of cyclic quadrilaterals. These MCQs are carefully designed to strengthen conceptual clarity,…
    🎓 Class 9 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
    Share on
    WhatsApp
    Telegram
    X / Twitter
    Facebook
    Instagram
    Threads
    Pinterest
    LinkedIn
    Quora
    Discord
    Reddit
    Email
    academia-aeternum.com/class-9/mathematics/circles/mcqs/ Copy link
    💡
    Exam tip: Sharing chapter notes with your study group creates a reinforcement loop. Teaching a concept is the fastest path to mastering it.

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