Learn › Class 9 CBSE · Mathematics › Circles
Circles — Class 9 CBSE Mathematics MCQs with Solutions
Free Class 9 CBSE Mathematics Circles MCQs with step-by-step solutions. Practise online on Prepizo — no login needed.
▶ Practise Circles online (free)
Sample questions with solutions
Q1 — easy
Longest chord of a circle is its:
A. Radius
B. Diameter ✓ Correct
C. Arc
D. Secant
Solution: Diameter passes through center and is longest chord.
Q2 — easy
Perpendicular dropped from center of a circle to a chord:
A. Bisects the chord ✓ Correct
B. Doubles the chord
C. Is equal to radius
D. Trisects chord
Solution: Perpendicular from center bisects chord into two equal halves.
Q3 — easy
Angle subtended by a semicircle arc at any point on remaining circumference is:
A. 60°
B. 90° (Right angle) ✓ Correct
C. 180°
D. 45°
Solution: Angle in a semicircle is a right angle (90°).
Q4 — easy
Angles subtended by a chord in the SAME segment of a circle are:
A. Supplementary
B. Equal ✓ Correct
C. Complementary
D. Unequal
Solution: Angles in same segment are equal.
Q5 — easy
Sum of either pair of opposite angles of a Cyclic Quadrilateral is:
A. 90°
B. 180° (Supplementary) ✓ Correct
C. 360°
D. 270°
Solution: Opposite angles of cyclic quadrilateral add to 180°.
Q6 — easy
If ABCD is a cyclic quadrilateral and ∠A = 70°, then ∠C =
A. 70°
B. 110° ✓ Correct
C. 90°
D. 120°
Solution: ∠A + ∠C = 180° → ∠C = 180° − 70° = 110°.
Q7 — easy
Equal chords of a circle subtend _______ angles at the center.
A. Complementary
B. Equal ✓ Correct
C. Supplementary
D. Unequal
Solution: Equal chords subtend equal central angles.
Q8 — easy
Chords equidistant from center of a circle are:
A. Equal in length ✓ Correct
B. Parallel only
C. Perpendicular
D. Unequal
Solution: Chords at equal distance from center are equal.
Q9 — easy
How many circles can pass through THREE given non-collinear points?
A. Only 1 unique circle ✓ Correct
B. Two circles
C. Infinitely many
D. None
Solution: Exactly one unique circle passes through 3 non-collinear points.
Q10 — easy
If a cyclic parallelogram is drawn inside a circle, it MUST be a:
A. Rhombus
B. Rectangle ✓ Correct
C. Trapezium
D. Square only
Solution: Opposite angles equal and supplementary → 90° → Rectangle.
Q11 — easy
A line segment joining any two points on a circle boundary is called a:
A. Secant
B. Chord ✓ Correct
C. Tangent
D. Sector
Solution: Chord joins two boundary points.
Q12 — easy
In a circle of radius 5 cm, distance of a 8 cm long chord from center is:
A. 3 cm ✓ Correct
B. 4 cm
C. 2.5 cm
D. 5 cm
Solution: Half chord = 4 cm. Right triangle: Distance = √(5² − 4²) = √9 = 3 cm.
Q13 — easy
Region bounded by an arc and two radii joining its endpoints to center is a:
A. Segment
B. Sector ✓ Correct
C. Chord
D. Arc
Solution: Sector is enclosed between two radii and an arc.
Q14 — medium
Angle subtended by an arc at the center is _______ the angle subtended by it at any point on remaining part of circle.
A. Equal to
B. Double (Twice) ✓ Correct
C. Half of
D. Thrice
Solution: Central angle = 2 × Inscribed angle.
Q15 — medium
If an arc subtends 80° at center, angle subtended by same arc at circumference =
A. 160°
B. 40° ✓ Correct
C. 80°
D. 90°
Solution: Inscribed angle = ½ × Central angle = 40°.