Tangent Lines in Circles

Tangent Lines

A tangent line to a circle is a line in the plane of the circle that intersects the circle in exactly one point.


The point where a circle and a tangent intersect is the point of tangency (Point B on the circle to the right).

Theorem

If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency.

Example 1: Finding Angle Measures

ML and MN are tangent to Circle O. Find the value of x.

Example 2:

A dirt bike chain fits tightly around two gears. The chain and gears form a figure like the one at the right. Find the distance between the centers of the gears.