1. 9-2 Tangents Theorem 9-1 (p. 333)
If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency. O P m

2. Corollary (p. 333) Tangents to a circle from a point are congruent.B P
Given: and are tangent to the circle at A and B.
By the corollary, ___ ___.

3. Theorem 9-2 p. 333
If a line in the plane of a circle is perpendicular to a radius at its outer endpoint, then the line is tangent to the circle. Q R l

4. Circumscribed polygons
When each side of a polygon is tangent to a circle,
the polygon is said to be circumscribed about the circle and
the circle is inscribed in the polygon.
Circumscribed polygons
Inscribed circles

5. A line that is tangent to each of two coplanar circles is called a common tangent.
A common internal tangent intersects the segment joining the centers.
A common external tangent does not intersect the segment joining the centers.

6. Tangent circles are coplanar circles that are tangent to the same line at the same point.
A and B are externally tangent.
C and D are internally tangent. A B C D

7. Name a line that satisfies the given description. B O P E D C
Name a line that satisfies the given description.
Tangent to P but not to O.
Common external tangent to O and P.
Common internal tangent to O and P.
Answers:

8. P Q R M N S
In the diagram, M and N are tangent to P and are tangent to N. N has diameter 16, PQ = 3, and RQ = 12. Find the following lengths: PM PR NS MQ SR NR

9. Assignments CW: p. 335 1-5 ( before end of class)
HW: p , 10, 14, 16-18