1. Tangent to a Circle
A tangent is a straight line that touches the circle at exactly one single point. The point where the line meets the circle is known as the point of contact.
- A circle can have infinitely many tangents.
- At any given single point on a circle, only one unique tangent can be drawn.
- A line that cuts through a circle crossing two distinct points is called a secant.
2. Core Circle Theorems (The Big Two)
These two properties are used to solve every mathematical problem in this chapter:
👉 Theorem 10.1 (Radius-Tangent Perpendicularity):
The tangent at any point of a circle is strictly perpendicular ($90^\circ$) to the radius through the point of contact.
👉 Theorem 10.2 (Equal Tangent Lengths):
The lengths of tangents drawn from an external point to a circle are completely equal. (If point $P$ is outside, and tangents touch at $A$ and $B$, then $PA = PB$).
CBSE Board Exam Classic Formula
Pythagoras Connection: Because the radius and tangent form a perfect $90^\circ$ right angle, you will almost always use the Pythagoras Theorem ($H^2 = P^2 + B^2$) to calculate missing lengths linking the center of the circle, the external point, and the tangent point!