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Class 10th Mathematics Chapter 10 Circles – PYQ

Previous year questions (PYQ) 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 previous year questions (PYQ) for Class 10th Mathematics Chapter 10 Circles?

This page lists previous year 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 PYQs free?

Yes, Notebook gives free previous year 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 pyq for quick revision?

You are on the right page: this pyq 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 Important Questions

Circles

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2 Marks 2023
State and prove the theorem: The tangent at any point of a circle is perpendicular to the radius through the point of contact.
Ans: Theorem: Tangent ⊥ radius at point of contact. Proof: Assume tangent not perpendicular. Then there exists a closer point on tangent inside circle — contradiction. So by shortest distance argument, radius ⊥ tangent.
3 Marks 2022
Two tangents drawn from an external point to a circle are equal. Prove.
Ans: Let PA and PB be tangents from P to circle with centre O. OA = OB (radii), OP common, angle OAP = angle OBP = 90°. By RHS congruence: ΔOAP ≅ ΔOBP → PA = PB.
5 Marks 2020
In a triangle, prove that the tangent lengths from each vertex to the inscribed circle sum in a meaningful way.
Ans: Let incircle touch AB, BC, CA at P, Q, R. Tangents from A: AP = AR; from B: BP = BQ; from C: CQ = CR. Then a+b+c = 2s (perimeter). Tangent sums equal semi-perimeter minus opposite side.
Other chapters in Mathematics · Class 10 View all Mathematics chapters →
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