Tangent line to a circle

Definition

Let $C$ be a circle in the Euclidean plane $\mathbb{R}^2$ , and let $T$ be a point of $C$ . A line $\ell$ is tangent to $C$ at $T$ if $\ell \cap C = \{T\}$ . The point $T$ is the point of tangency.

Remarks

A line meets a circle in two points, in one point or in no point. A line with two common points is a secant line. For the circle $(x - a)^2 + (y - b)^2 = r^2$ and a point $(x_1, y_1)$ on it, the tangent at this point has the equation $(x - x_1)(x_1 - a) + (y - y_1)(y_1 - b) = 0$ . The tangent at $T$ is the line through $T$ perpendicular to the radius to $T$ . See a tangent is perpendicular to the radius. From a point outside the circle there are exactly two tangent lines to the circle.

Reading path

To understand this page from the ground up, read these 3 pages in order. The foundations come first.

Show the path as a graph

Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.

no evidence level

Circle concept
Line concept
Tangent line to a circle definition

Tag	`0C6THFRMZR`
URI	`m2://0C6THFRMZR`
Kind	definition
Writing	W1 stated
MSC	51M04
Defines	Tangent line to a circle
Uses	Circle, Line

Tangent line to a circle

Definition

Remarks

Reading path

Further reading

What this page needs for W2

What links here