1. Section 9-2
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.
radius
tangent
Right angle

3. Theorem 9-2
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.
This is the converse of theorem 9-1.
Point of tangency

4. . Example 1 Use R with tangent OT to complete:
1.) If OR = 6 and OT = 8,
then RT = _____.
2.) If m<OTR = 45, and
OT = 4, then RT = _____.
3.) If RO = 5, and OT = 12
then ET = _____. R E O T

5. Corollary Tangents to a circle from a point are congruent C Segment AC
is congruent to
Segment AB B

6. Inscribed and Circumscribed
Circumscribed about the circle
When a polygon has all sides being a tangent of a circle

7. Inscribed and Circumscribed
Inscribed in the polygon
The same situation as before, the polygon has a circle inside that meets each side at a point of tangency

8. Common tangents
With two circles we draw an invisible line connecting the centers
A common tangent that crosses this line is an internal tangent
A common tangent that does not cross this line is an external tangent
external
internal

9. Example 2…think about it…
What do you think is true about common internal tangents RS and TU? R U G
RG = TG S +
GS = GU T
RG + GS = TG + GU
RS = TU

10. Tangent Circles
Two circles can be tangent to each other if they share exactly one point
Internally tangent
Externally tangent

11. . . Example 3 Name a line that satisfies the given description
1.) tangent to P but
not to Q.
2.) Common external tangent
to both circles
3.) Common internal tangent A B Q P W E C D

12. Example 4 . .
In the diagram, M and N are tangent at P. PR and SR are tangents to N N has diameter 16, PQ = 3, and RQ = 12
1.) PM = ____ 2.) MQ = ____
3.) PR = ____ 4.) SR = ____
5.) NS = ____ 6.) NR = ____ . . R P Q M N S

13. HW: pg (1-11)
The
End