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

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

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

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

Section 10.1: Use Properties of Tangents How many common tangents do these circles have? Draw them 1. 2. 3. 4.

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

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

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

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

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