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Circles Quiz - CBSE Class 9 Mathematics

Free practice quiz: Circles (CBSE Class 9 Mathematics). 16 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 9 Mathematics practice quiz has 16 multiple-choice questions on Circles, and 16 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Start quiz: 16 questions, free

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Parts of a Circle

  • A circle is the set of all points in a plane at a fixed distance from a fixed point, the centre.
  • The radius joins the centre to the circle. A chord joins two points on the circle.
  • A diameter is a chord through the centre. It is the longest chord and equals two radii.
Diameter and radius
\[d = 2r\]
Radius from diameter
\[r = \frac{d}{2}\]

Common mistake: Using the diameter in place of the radius in formulas. Always halve the diameter first.

Circumference, Area and Arc Length

  • Circumference is the distance around the circle. Area is the region enclosed by it.
  • An arc with central angle θ is the fraction θ/360 of the whole circumference.
Circumference
\[C = 2\pi r\]
Area
\[A = \pi r^2\]
Arc length
\[l = \frac{\theta}{360^\circ} \times 2\pi r\]
Radius from area
\[r = \sqrt{\frac{A}{\pi}}\]

Common mistake: Mixing up 2πr and πr². Area uses r squared, while circumference uses 2 times r.

Chord Properties

  • A perpendicular from the centre to a chord bisects the chord. So a diameter perpendicular to a chord halves it.
  • For two intersecting circles, the line joining the centres is the perpendicular bisector of the common chord.
Perpendicular bisects chord
\[OM \perp AB \Rightarrow AM = MB\]
Half-chord, radius, distance
\[r^2 = d^2 + \left(\frac{c}{2}\right)^2\]

Common mistake: Assuming any line through the centre bisects a chord. It must be perpendicular to the chord.

Angle at Centre Theorem

  • The angle an arc subtends at the centre is double the angle it subtends at any point on the remaining circle.
  • Angles in the same segment are equal. The angle in a semicircle is a right angle.
Centre vs circumference
\[\angle AOB = 2\angle ACB\]
Angle in a semicircle
\[\angle ACB = 90^\circ\]

Common mistake: Doubling the angle at the centre instead of halving it to find the angle at the circumference.

Tangents and Power of a Point

  • A tangent touches the circle at one point. It is perpendicular to the radius at that point.
  • Two tangents from an external point are equal in length.
  • Power of a point P is d² − r², where d is its distance from the centre. Outside the circle, this equals the tangent length squared.
Tangent length (Pythagoras)
\[PT^2 = d^2 - r^2\]
Power of a point
\[\text{Power}(P) = d^2 - r^2 = PT^2\]
Tangents and radii angles
\[\angle APB + \angle AOB = 180^\circ\]

Common mistake: Forgetting the right angle at the point of contact, or adding squares instead of subtracting when finding the radius or tangent.

Exam tips

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

  1. What is the definition of a circle?

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    Answer: B. A closed figure with all points equidistant from a center

    A circle is defined as a closed curve with all points equidistant from the center.

  2. What is the circumference of a circle with a radius of 4 cm (use π = 3.14)?

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    Answer: A. 25.12 cm

    The circumference is calculated using 2πr. Therefore, 2 x 3.14 x 4 = 25.12 cm.

  3. What is the area of a circle with a radius of 7 cm? (use π = 3.14)

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    Answer: A. 154 cm²

    Area is calculated using πr². Therefore, 3.14 x 7 x 7 = 154 cm².

  4. What is the length of the arc of a circle with a radius of 5 cm and a central angle of 72° (use π = 3.14)?

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    Answer: A. 6.28 cm

    Length of the arc is calculated using the formula (θ/360) x 2πr. Therefore, (72/360) x 2 x 3.14 x 5 = 6.28 cm.

  5. If a circle's area is 78.5 cm² (using π = 3.14), what is the radius?

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    Answer: A. 5 cm

    Area = πr², thus 3.14r² = 78.5, giving r² = 25 and r = 5 cm.

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More questions in this quiz

Answers and explanations are in the full quiz.

  1. What is the radius of a circle?
  2. If the diameter of a circle is 10 cm, what is its radius in cm?
  3. Which line segment represents the diameter of a circle?
  4. In the circle, if chord AB is perpendicular to diameter CD at point E, what can be said about AE and EB?
  5. Which theorem states that the angle subtended by an arc at the center is twice the angle subtended at the circumference?
  6. If an arc subtends an angle of 60° at the center, what is the measure of the angle it subtends at the circumference?
  7. In a circle, what is the relationship between a tangent and the radius at the point of contact?
  8. From a point 13 cm away from the center of a circle, the length of the tangent drawn is 12 cm. What is the radius of the circle?
  9. What is the measure of the angle between two tangents drawn from an external point to a circle, if the angle between their radii is 60°?
  10. What is the power of a point with respect to a circle?
  11. In two intersecting circles, if AB is a common chord and point P is the center of the first circle, which statement holds?

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