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Class 10th Mathematics Chapter 10 Circles – Important Questions

Important questions with answers for Class 10th Mathematics Chapter 10 Circles, based on the NCERT CBSE syllabus.

Topics covered in Circles

Frequently asked questions

Where can I find important questions for Class 10th Mathematics Chapter 10 Circles?

This page lists important questions with answers for Circles. Topics covered: Tangent to a circle, Tangent-radius theorem, Number of tangents from external point, Length of tangent.

Are Circles important questions free?

Yes, Notebook gives free NCERT CBSE important questions for Class 10 Mathematics.

How to prepare Circles for Class 10 Mathematics exams?

Read the Circles notes first, revise the key topics (Tangent to a circle, Tangent-radius theorem, Number of tangents from external point, Length of tangent), then practise the important questions and previous year questions (PYQ) for this chapter.

Where can I find Class 10th Mathematics Chapter 10 Circles important questions for quick revision?

You are on the right page: this important questions page for Circles covers Class 10 Mathematics for the CBSE exam 2026-27. Use the tabs on this chapter for notes, important questions and PYQ.

Is Class 10th Mathematics Chapter 10 Circles important for the CBSE exam 2026-27?

Circles is part of the Class 10 Mathematics NCERT CBSE syllabus. Notebook gives notes, important questions and PYQs for it, free.

Also see: Class 10th Mathematics Chapter 10 Circles Notes · Class 10th Mathematics Chapter 10 Circles PYQ

Circles

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1 Mark
How many tangents can be drawn to a circle from an external point?
Ans: Exactly two tangents can be drawn to a circle from an external point.
2 Marks
A tangent PQ at point P of a circle of radius 5 cm meets line through centre O at Q such that OQ = 13 cm. Find PQ.
Ans: OP ⊥ PQ (radius ⊥ tangent). PQ² = OQ² – OP² = 169 – 25 = 144. PQ = 12 cm.
3 Marks
Prove that the tangents drawn from an external point to a circle are equal in length.
Ans: Let PA and PB be tangents from external point P to circle with centre O. OA⊥PA and OB⊥PB (radius ⊥ tangent). In △OAP and △OBP: OA=OB (radii), OP=OP (common), ∠OAP=∠OBP=90°. By RHS congruence: △OAP ≅ △OBP. Therefore PA = PB. ✓
Other chapters in Mathematics · Class 10 View all Mathematics chapters →
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