1. Tangents

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

3. Consider the following diagram:

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

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

6. Example 1:

7. 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

8. Example:

10. 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

11. Example
x+4 y 10
y-5

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

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