1. Chapter 10: Properties of Circles
Section 10.1: Use Properties of Tangents

2. Section 10.1: Use Properties of Tangents
Secant: a line that intersects a circle in two points
Tangent: a line that intersects the circle in exactly one point (Point of tangency)
Secant
Tangent
Point of tangency

3. Section 10.1: Use Properties of Tangents
Intersection of 2 Coplanar Circles
1 Point of Intersection
(Tangent Circles)
2 Points of Intersection
0 Points of Intersection
Concentric Circles: coplanar circles that have a common center

4. Section 10.1: Use Properties of Tangents
Common Tangent: A line, segment, or ray that is a tangent to two circles

5. Section 10.1: Use Properties of Tangents
How many common tangents do these circles have? Draw them

6. Section 10.1: Use Properties of Tangents
Theorem 10.1: A line is tangent to a circle iff the line is perpendicular to the radius drawn to the point of tangency A Q P B
AB is tangent to circle P iff AB PQ

7. Section 10.1: Use Properties of Tangents
CD is tangent to circle F. Find the radius r of circle F when CF = 13 and CD = 12.
AB is tangent to circle C. Find the radius r of circle C when AC = 10 and AB = 8 F 13 r C 12 D 10 C A 8 B

8. Section 10.1: Use Properties of Tangents
Theorem 10.2: Tangent segments from a common external point are congruent R P S T
If RS and ST are tangent segments, then RS ≅ ST

9. Section 10.1: Use Properties of Tangents
AB and BC are tangent to circle D. If AB = 16 and BC = 2x – 4, find the value of x. A 16 D B
2x – 4 C

10. Section 10.1: Use Properties of Tangents
Homework: Pg. 655 #3-26 (all)