Symmetries of a Circle Class 9 Maths | I'm Up and Down, and Round and Round

Understand it

If a circle is folded along any diameter, the two halves match exactly. If it is rotated around its centre, it still looks the same because all boundary points remain at the same distance from the centre.

Example

A wheel rotated by 40 degrees about its centre still has the same circular outline. A fold along any line through the centre divides the circle into two equal halves.

Formula and rule

Reflection symmetry: every diameter is an axis of symmetry.

Rotational symmetry: a circle matches itself after rotation about the centre by any angle.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

If a line l cuts a circle into two mirror-image halves and passes through centre O, l is a diameter and an axis of symmetry.

Method you can reuse

1Look for the centre.
2Check if the proposed mirror line passes through it.
3For rotation, check whether the rotation is about the centre, not about a point on the circle.

Sketch it in your answer

Draw several diameters through the same centre and show each one splitting the circle into equal halves.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Why is any diameter a line of symmetry of a circle?

Think first, then show answer

Any diameter is a line of symmetry because it passes through the centre and divides the circle into two matching semicircles.

Common wrong answer

Saying a circle has only two lines of symmetry.

Why it loses marks: Infinitely many diameters can be drawn through the centre.

Don't mix this up

Students sometimes think only horizontal and vertical diameters are lines of symmetry. Actually, every diameter is a line of symmetry.

Exam tip

For symmetry questions, check whether the line passes through the centre. A chord not passing through the centre is not a line of symmetry of the whole circle.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Students may be asked to identify lines of symmetry, rotational symmetry, or explain why a given line is not a symmetry line.

1
Enough for 1 mark
A circle has reflection symmetry about every diameter and rotational symmetry about its centre for any angle of rotation.
2
Add for 2 marks
Example: A wheel rotated by 40 degrees about its centre still has the same circular outline. A fold along any line through the centre divides the circle into two equal halves.
3
Add for 3 marks
If a circle is folded along any diameter, the two halves match exactly.

Use the concept graph around this idea instead of revising it in isolation.

Definition of a Circle

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

Chord and Its Properties

A chord is a line segment joining two points on a circle. The perpendicular from the centre of a circle to a chord bisects the chord, and equal chords are equidistant from the centre.

Three Points Determine a Circle

One and only one circle can pass through three non-collinear points. Its centre is found at the intersection of perpendicular bisectors of two joining segments.

Angle Subtended by Arc/Chord at Centre vs at Circumference

The angle subtended by an arc or chord at the centre of a circle is twice the angle subtended by it at any point on the remaining part of the circle.

Previous: Definition of a Circle Next: Chord and Its Properties Back to full mind map

Symmetries of a Circle

Understand it

See it worked out

Check yourself

Write it in the exam

Practice this concept with focused MCQs

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Symmetries of a Circle

Understand it

See it worked out

Check yourself

Write it in the exam

Related concepts

Practice this concept with focused MCQs

Help improve this page