14 2 tangents to a circle lesson

1. Use Properties of Tangents
14-2

2. Vocabulary
•Circle- the set of all pts in a plane that are
equidistant from a given pt. called the center of
the circle.
•Radius- segment whose endpoints are the
center and any point on the circle
•Diameter- a chord that contains the center of the
circle.
•Two polygons are similar if corresponding
angles are congruent and corresponding side
lengths are proportional. ΔABC ~ ΔDEF

3. P
P is the
center of
the circle
A
B
Segment AB
is a diameter
C
Segments AP,
PB, and PC are
radii

4. Chord
•Chord- a segment whose endpoints are
on the circle.
A B

5. Secant
•Secant- a line that intersects a circle in 2
pts
A
B

6. Tangent
•Tangent- a line in the plane of the circle
that intersects the circle in exactly one
point, called the point of tangency.

7. •Point of tangency- point where tangent
intersects a circle
T
Point T is the
point of tangency

8. Example
tell whether the segment is best
described as a chord, secant,
tangent, diameter or radius
•Segment AH
•Segment EI
•Segment DF
•Segment CE
A
B
C
D
E
F
G
H
I

9. Example
tell whether the segment is best
described as a chord, secant,
tangent, diameter or radius
•Segment AH
•Segment EI
•Segment DF
•Segment CE
A
B
C
D
E
F
G
H
I
tangent
Diameter
Chord
radius

10. Tangent circles- circles that intersect in
one point
Concentric circles- circles
that have a common center
but different radii lengths

11. Common internal tangent- a tangent that
intersects the segment that connects the
centers of the circles
Common external tangent- does not
intersect the segment that connects the
centers

12. Example
Common internal or external
tangent?

13. Example
Common internal or external
tangent?
external

14. Theorem 14-4
•In a plane, a line is tangent to a circle if
and only if it is perpendicular to a radius of
the circle at its endpoint on the circle.

15. Example
Is segment CE tangent to circle D?
Explain
D
E
C
11
45
43
Remember in order to find if a
line is tangent we need to
know if there is a 90 degree
angle

16. Example
Is segment CE tangent to circle D?
Explain
D
E
C
11
45
43
11
2
+43
2
=45
2
121+1849=2025
1970=2050
NO
Let’s use the
Pythagorean
Theorem

17. Example
solve for the radius, r
A
B
C
r
r
28ft
14ft

18. Example
solve for the radius, r
A
B
C
r
r
28ft
14ft
r
2
+28
2
=(r+14)
2
r
2
+ 784=r
2
+ 28r+196
784=28r+196
588=28r
21=r

19. Theorem 14-6
•Tangent segments from a common
external point are congruent.

20. Example
segment AB is tangent to circle C
at pt B. segment AD is tangent to
circle C at pt D. Find the value of X
C
B
D
A
x
2
+8
44

21. Example
segment AB is tangent to circle C
at pt B. segment AD is tangent to
circle C at pt D. Find the value of X
C
B
D
A
x
2
+8
44
x
2
+8=44
x
2
=36
X=6