1. Chapter 9
Section-2
Tangents

2. 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.

3. 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

4. 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

5. 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.

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

7. 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

8. :9-2 Tangents: Homework
Page 335
Class Ex: 1-4
Written Ex: 1-11, 16-18