Do Now Find the area and circumference of each circle 1) 2)

10.1 Use Properties of Tangents Objective: To use properties of tangents

Definition of a circle and its center A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. Circle B B

Circle Vocabulary Tangent: A line in the plane of a circle that intersects the circle in exactly one point (the point of tangency).

Circle Vocabulary Center: C and G Radius: a segment whose endpoints are the center and any point on the circle. (AC, CD, CH, GE, GF) Chord: a segment whose endpoints are on a circle. (AB and AD)

Circle Vocabulary Diameter: a chord that contains the center of the circle. (AD) Secant: a line that intersects a circle in two points. (AB)

Circle Vocabulary Common internal tangent: a line that is tangent to two circles & goes between two circles. (tangent HF is internal) Common external tangent: a line that is tangent to two circles & lies outside both circle. (tangent DE is external)

Example 1: Common Tangents

Theorem In a plane, a line is tangent to a circle if and only if the line is perpendicular to a radius of the circle at its endpoint on the circle. CB is tangent to circle A at point C which is the point of tangency. This makes CB perpendicular to AC. C B A

Example 2:

Example 3:

Theorem Tangent segments from a common external point are congruent. C B