Geometry: Circles

Tangent Lines and Secant Lines

Tangent Lines

A tangent line is a line that intersects a circle at one point. Such a line is said to be tangent to that circle. The point at which the circle and the line intersect is the point of tangency.

Figure %: A tangent line
In the figure above, the line l is tangent to the circle C. Point T is the point of tangency.

When a radius of a circle is drawn to a point of tangency (from the center, of the circle, of course), that radius is perpendicular to the tangent line containing that point of tangency. This means that for any tangent line, there exists a perpendicular radius.

Figure %: A tangent line is perpendicular to a radius

A tangent segment is a segment with one endpoint at the point of tangency and its other endpoint somewhere on the tangent line. A tangent segment is also perpendicular to the radius of the circle whose endpoint is the point of tangency.

Figure %: A tangent segment

Secant Lines

A secant line is a line that intersects a circle at two points. Every secant line, therefore, contains a chord of the circle it intersects.

Figure %: A secant line

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