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Circles — Class 10 CBSE Mathematics MCQs with Solutions
Free Class 10 CBSE Mathematics Circles MCQs with step-by-step solutions. Practise online on Prepizo — no login needed.
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Sample questions with solutions
Q1 — easy
How many tangents can be drawn to a circle from a point on the circle?
A. 0
B. 1 ✓ Correct
C. 2
D. infinite
Solution: Exactly one tangent at a point on the circle.
Q2 — easy
The tangent at any point of a circle is ___ to the radius at the point of contact.
A. parallel
B. perpendicular ✓ Correct
C. equal
D. inclined at 45°
Solution: The tangent is perpendicular to the radius.
Q3 — easy
How many tangents can be drawn from an external point to a circle?
A. 0
B. 1
C. 2 ✓ Correct
D. infinite
Solution: Exactly two tangents.
Q4 — hard
If two tangents to a circle are parallel, the points of contact are the endpoints of a:
A. chord
B. diameter ✓ Correct
C. radius
D. tangent
Solution: Parallel tangents touch at diameter endpoints.
Q5 — hard
The distance between the centres of two circles of radii 5 cm and 3 cm touching externally is:
A. 2 cm
B. 4 cm
C. 8 cm ✓ Correct
D. 15 cm
Solution: Sum of the radii.
Q6 — hard
A tangent PQ at point P of a circle of radius 5 cm meets a line through the centre at Q so that OQ = 13 cm. Find PQ.
A. 10 cm
B. 11 cm
C. 12 cm ✓ Correct
D. 13 cm
Solution: √(169−25) = 12 cm.
Q7 — medium
A line intersecting a circle at two points is called a:
A. tangent
B. secant ✓ Correct
C. radius
D. arc
Solution: A secant cuts the circle twice.
Q8 — medium
The angle between a tangent and the radius at the point of contact is:
A. 0°
B. 45°
C. 90° ✓ Correct
D. 180°
Solution: They are perpendicular.
Q9 — medium
Two concentric circles have radii 5 cm and 3 cm. The length of a chord of the larger circle touching the smaller is:
A. 4 cm
B. 6 cm
C. 8 cm ✓ Correct
D. 10 cm
Solution: Half chord = √(25−9) = 4, so chord = 8 cm.