Chapter 9 Section-2 Tangents

Theorem 9-1: If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency. Theorem 9-2: If a line in a plane of a circle is perpendicular to a radius at its outer endpoint, then the line is tangent to the circle. Corollary: Tangents to a circle from a point are congruent.

Common tangent: A line that’s tangent to each of 2 coplanar circles A common tangent (internal) intersects the segment joining the centers. A common tangent (external) doesn’t intersect the segment joining the centers. R A P Q S D Q E P B U C T

Internally tangent circles: Externally tangent circles: Tangent circles: coplanar circles that are tangent to the same line at the same point Internally tangent circles: Externally tangent circles: R S Q P

Inscribed circle: when each side of the polygon is tangent to a circle These figures can be described as being either an inscribed circle or a circumscribed polygon. Circumscribed polygon: when each side of the polygon is tangent to a circle This figure cannot be described as being either an inscribed circle or a circumscribed polygon.

Draw 2 circles with the following number of common tangents: 1 2 3 4

Name a line that satisfies the given description: Name a line that satisfies the given description: A B O P E D C Tangent to circle P but not to circle O: Common external tangent to circle O & circle P: Common internal tangent to circle O & circle P: OB CD AE P R S Q M N 3 12 8 4 4 5 15 4. PM = _____ 5. MQ = _____ 6. PR = _____ 7. SR = _____ 5. NS = _____ 6. NR = _____ 15 8 17

:9-2 Tangents: Homework §9.2 Classroom Exercises (p. 335) #1-5 §9.2 Classroom Exercises (p. 335) #1-5 §9.2 Written Exercises (p. 335-336) #1-11, 14, & 16-18