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Unit: Circles pt 1
Note Taking Guide:
Lesson 2: Tangents and Similar Triangles
Tangents and Similar Triangles
Concentric
Circles
Externally
Tangent Circles
Internally Tangent
Circles
Common Internal
Tangents
Common External
Tangents
Unit: Circles pt 1
Internally Tangent Circles:
Common External Tangents:
Common Internal Tangents:
Note Taking Guide:
Lesson 2: Tangents and Similar Triangles
Externally Tangent Circles:
Unit: Circles pt 1
Note Taking Guide:
Lesson 2: Tangents and Similar Triangles
Tangent Theorem #2: If two segments from the same exterior point
are tangent to a circle, then they are congruent.
“Party Hat” rule!
1. x  __________
2. x  __________
3. x  __________
4. NP  __________
Triangles are similar if they have the same shape, but not necessarily the same size.
Properties of similar triangles:
 corresponding angles are the same
 corresponding sides are in proportion
We can prove triangles are similar by:
 Angle-Angle (two angles congruent to two angles of another triangle)
 Side-Side-Side (all three sides in proportion to all three sides of another
triangle)
 Side-Angle-Side (two proportional sides with congruent angle in between)
Unit: Circles pt 1
Note Taking Guide:
Lesson 2: Tangents and Similar Triangles
Your Turn:
The diameter of a circle is given. Find the radius.
1.__________
1. d  17 in
2. d  18cm.
2.__________
The radius of a circle is given. Find the diameter.
3.__________
3. r 
4. r  8.3 ft.
23 cm.
4.__________
Using the diagram, name the following using the correct notation.
5.__________
Center
6.__________
Chord
7.__________
Diameter
8.__________
Radius
9.__________
Secant
10._________
Common internal tangent
11._________
Common external tangent
12._________
M
P
F
T
C
J
A
G
L
Point of tangency
B
D
E
Give the number of common tangents that could be drawn in each diagram.
13._________
14._________
15._________
16._________
13.
14.
15.
16.
Unit: Circles pt 1
Note Taking Guide:
Lesson 2: Tangents and Similar Triangles
For each figure below, identify the number of points of intersection and the number of common
internal and external tangents:
Points of
intersection
# Common internal
tangents
# Common external
tangents
17. ____________
_______________
______________
18. ____________
_______________
______________
19. Make a rule!
Diagram