**Tangents from an External Point**

Tangent segments from a common point external to a circle have the same length.

We can prove this as follows:

Let *O* be the center of the circle, *P* the common endpoint of the tangent segments, and *A* and *B* their points of tangency. Then angles *OAP* and *OBP* are right angles (because tangents are perpendicular to radii). Since segments *OA* and *OB* are radii, they are the same length. *OP* is a common hypotenuse of right triangles *OAP* and *OBP*, so these triangles are congruent by **HL**. Therefore *AP* = *BP* since they are corresponding parts.