Tangents

A line is tangent to a circle if it intersects the circle in exactly one point. This point is called the point of tangency.

Consider the following diagram:

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

Example: If RT is tangent to Circle O, Then ORRT

Example 1:

The converse of the last theorem is also true The converse of the last theorem is also true. This means: In a plane, if a line is perpendicular to a radius of a circle at the endpoint on the circle, then the line is a tangent of the circle. If ORRT, RT is tangent to Circle O

Example:

Theorem 10.11: If two segments from the same exterior point are tangent to a circle, then the two segments are congruent. Example: ABCB

Example x+4 y 10 y-5

Circumscribed polygons: A polygon is circumscribed about a circle if each side of the polygon is tangent to the circle. Example:

Example: Triangle HJK is circumscribed about circle G. Find the Perimeter of HJK if NK = JL+29. 45 JL + 29 18