Circles
Rajasthan Board · Class 10 · Mathematics
Quick revision notes for Circles — Rajasthan Board Class 10 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Line and Circle Relationships
- Three possible positions of a line with respect to a circle: non-intersecting, secant, and tangent
- Non-intersecting line: No common points with the circle
- Secant: Line intersecting circle at two distinct points
Tangent Properties and Theorems
- Theorem 10.1: Tangent is perpendicular to radius at point of contact
- At any point on a circle, there is exactly one tangent
- The radius through point of contact is called the normal to the circle
Number of Tangents from Different Points
- From point INSIDE circle: Zero tangents possible
- From point ON circle: Exactly one tangent
- From point OUTSIDE circle: Exactly two tangents
Theorem Proofs and Applications
- Proof of Theorem 10.1 uses the fact that tangent gives shortest distance from center to line
- Proof of Theorem 10.2 uses congruent right triangles (RHS congruency)
- Alternative proof using Pythagoras theorem: PT₁² = PO² - r² = PT₂²
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Circles covers several key topics that are frequently asked in Rajasthan Board Class 10 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
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