Class 10 · Chapter 10

Circles

Tangents to a circle, number of tangents from a point, tangent-radius property.

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Tip: open the NCERT PDF for the original chapter text alongside the notes here.
Detailed theory
A tangent to a circle is a line that touches the circle at exactly one point (the point of contact). A secant intersects the circle at two points. As a secant rotates about a fixed point, in the limiting position it becomes a tangent.
Key concepts & formulas
01
Tangent is perpendicular to the radius at the point of contact.
02
From an external point exactly 22 tangents to a circle exist, and they are equal in length.
03
From a point on the circle exactly 11 tangent exists.
04
Length of tangent from external point =d2r2= \sqrt{d^2 - r^2} where dd is distance from centre.
05
Angle between two tangents from an external point is supplementary to the central angle.
06
Two circles have 0044 common tangents depending on relative position.
Gyaan Maths — CBSE Class 6-10, built for board-toppers.
v1.1 · Feb 2026