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🧾 CBSE · Class 10

Class 10 Maths: Circles Worksheet (with Answers)

A free, print-ready worksheet on Circles for CBSE Class 10 Maths, with a matching answer key. Use the sample below, or build your own with the exact mix of questions you need — no login, no ads.

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Sample worksheet

7 of 19 questions from this chapter. Generate your own for the full set, more variations, and a clean print layout.

  1. 1. A tangent to a circle touches it at:
    • (a) three points
    • (b) exactly one point
    • (c) two points
    • (d) no point
  2. 2. The angle between a tangent and the radius at the point of contact is:
    • (a) 45°
    • (b) 180°
    • (c) 90°
    • (d) 60°
  3. 3. The number of tangents that can be drawn from an external point is:
    • (a) 2
    • (b) infinite
    • (c) 3
    • (d) 1
  4. 4. The two tangents drawn from an external point are:
    • (a) unequal
    • (b) perpendicular
    • (c) parallel
    • (d) equal in length
  5. 5. How many tangents can a circle have in all?
  6. 6. State the angle between a tangent and the radius at the point of contact.
  7. 7. Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact (state the idea).
View answers
  1. 1. (b) exactly one point — A tangent touches at exactly one point.
  2. 2. (c) 90° — The tangent is perpendicular to the radius there.
  3. 3. (a) 2 — Exactly two tangents from an external point.
  4. 4. (d) equal in length — Tangents from an external point are equal in length.
  5. 5. Infinitely many — one at every point of the circle.
  6. 6. 90° (they are perpendicular).
  7. 7. Take the centre O and tangent at point P. Any point Q on the tangent other than P lies outside the circle, so OQ > OP. Hence OP is the shortest distance from O to the tangent, and the shortest distance is the perpendicular — so OP ⟂ the tangent.
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How it works

Every question is drawn from StudyMatic’s own Maths bank for Circles — nothing is auto-generated or invented. Pick how many of each type you want, add your own questions if you like, choose 1–4 paper sets for anti-cheating, and print the worksheet and answer key separately or save them as PDF.

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FAQ

Is this Class 10 Maths worksheet on Circles free?
Yes — it is completely free, with no login and no ads. You can print it or save it as a PDF, and generate unlimited variations.
Does the Circles worksheet come with answers?
Yes. Every worksheet has a separate answer key with the correct answers, short explanations and marks, so it is ready for marking.
Can I choose how many questions and which types?
Yes. Open the generator for this chapter and set how many MCQs, short, long and HOTS questions you want; totals and marks update live, and you can swap any single question.
Which board and class is this for?
This worksheet is aligned to CBSE Class 10 Maths, chapter “Circles”.