Access the official NCERT Class 10 Mathematics textbook for Chapter 10 – Circles PDF. This chapter builds upon your previous knowledge of circles and focuses on tangents: you’ll learn that a tangent intersects a circle at exactly one point and is perpendicular to the radius. It also covers how many tangents can be drawn from a point, the properties of tangents from an external point (they are equal in length), and several important theorems for problem-solving.
Chapter Highlights:
- Definitions: circle, radius, diameter, chord, arc, sector, segment
- Locus view: line–circle interactions (no intersection, secant, tangent)
- Tangent to a circle: uniqueness at a point and perpendicularity to radius
- Theorems on tangents:
- Single tangent from a point on the circle
- Two equal tangents from an external point
- Converse theorems & angle subtended in circumscribing quadrilaterals
- Length of tangent from an external point (Pythagorean approach)
- Construction problems: drawing tangents from points inside, on, and outside the circle