Circles PYQs
Practise tangents, tangent properties, and circle theorems through focused CBSE previous-year questions.
Use these previous-year questions to revise the tangent-radius relationship, the number of tangents from a point, and equal tangents from an external point. Follow each topic to practise theorem-based proofs, diagram interpretation, and the concise reasoning expected in CBSE board answers.
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CBSE Board Exam Blueprint & Topic Weightage: Circles
In the Class 10 CBSE Board Examination, Circles is a high-yielding component of Unit 4: Geometry, consistently carrying 4 to 6 marks in the annual 80-mark written board paper. Recurring question formats observed over past board papers include:
- Section A (1 Mark MCQ): Angle between tangent and radius at point of contact (\(90^\circ\)), number of tangents from points inside, on, or outside a circle, and angle subtended by tangents at center.
- Section B / C (2 or 3 Marks): Applying Theorem 10.1 (tangent perpendicular to radius) and Theorem 10.2 (equal tangent lengths from an external point) to find lengths, angles, and chord relationships.
- Section D (5 Marks Proof): Proving that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the center, or proving \(AB + CD = AD + BC\) for circumscribing quadrilaterals.
Key Revision Tips & Common Pitfalls
Theorem 10.2 is frequently asked as a direct theorem proof. Remember that radii drawn to points of contact create right angles, which often allows you to apply Pythagoras theorem in right triangles formed by radius, tangent, and line from center to external point.