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

2. 10.1 Use Properties of Tangents
Objective: To use properties of tangents

3. 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

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

5. 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)

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

7. 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)

8. Example 1: Common Tangents

9. 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

10. Example 2:

11. Example 3:

12. Theorem Tangent segments from a common external point are congruent. CB