Over Lesson 10–4
Section 10.4 (part 2) WB Pg. 31 #1-12

a
c
1. a = 100°
3. c = 23°
5. e = 50°
7. g = 50°
9. i = 48°
2. b = 40°
4. d = 82°
6. f = 84°
8. h = 84°

P

b
42
80
e 
f
46
h

i

g
c d
10. a = 35°
12. c = 25°
14. e = 35°
16. g = 50°
d
11. b = 70°
13. d = 70°
15. f = 25°
70
e 
f

P
50
b
50
a g

A tangent is a line in the same plane as a circle that
intersects the circle in exactly one point, called the
point of tangency.
AB is tangent to C at point A.
AB and AB are also called tangents.
A common tangent is a line, ray, or segment that
is tangent to two circles in the same plane.
In each figure below, in l is a common tangent of
circles F and G.
Identify Common Tangents
A. Using the picture on the right, draw the common
tangents. If no common tangent exists, state no
common tangent.
Identify Common Tangents
B. Using the figure to the right, draw the common
tangents. If no common tangent exists, state no
common tangent.
Identify a Tangent
A)
B)
Use a Tangent to Find Missing Values
A)
B)
Watch:
Think of the 2 tangents as a party hat!
The sides of the hat are congruent 
Use Congruent Tangents to Find Measures
A)
B)
Circumscribed Polygons
A polygon is circumscribed about a circle if every side
of the polygon is tangent to the circle.
Find Measures in Circumscribed
Polygons
A)
B)
C)
XY = 22
YZ = 15
ZW= 16
Find XW.
Y
Z
X
W
1.
2.
3.
4.
Complete WB Pg. 28 #1 and 4
Complete WB Pg. 31 #10-16 (choose any three)
Complete WB Pg. 27 #1-6
SKILLS CHECK when 15 minutes are left
HW: Anything from 1-3 that is not finished!
Content Standards
G.CO.12 Make formal geometric constructions with a
variety of tools and methods (compass and
straightedge, string, reflective devices, paper folding,
dynamic geometric software, etc.).
G.C.4 Construct a tangent line from a point outside a
given circle to the circle.
Mathematical Practices
1 Make sense of problems and persevere in solving
them.
2 Reason abstractly and quantitatively.
You used the Pythagorean Theorem to find
side lengths of right triangles.
• Use properties of tangents.
• Solve problems involving circumscribed
polygons.
• tangent
• point of tangency
• common tangent
Five-Minute Check (over Lesson 10–4)
CCSS
Then/Now
New Vocabulary
Example 1: Identify Common Tangents
Theorem 10.10
Example 2: Identify a Tangent
Example 3: Use a Tangent to Find Missing Values
Theorem 10.11
Example 4: Use Congruent Tangents to Find Measures
Example 5: Real-World Example: Find Measures in
Circimscribed Polygons
Over Lesson 10–4
Refer to the figure. Find m1.
A. 60
B. 55
C. 50
D. 45
Over Lesson 10–4
Refer to the figure. Find m2.
A. 30
B. 25
C. 20
D. 15
Over Lesson 10–4
Refer to the figure. Find m3.
A. 35
B. 30
C. 25
D. 20
Over Lesson 10–4
Refer to the figure. Find m4.
A. 120
B. 100
C. 80
D. 60
Over Lesson 10–4
find x if mA = 3x + 9 and mB = 8x – 4.
A. 10
B. 11
C. 12
D. 13
Over Lesson 10–4
The measure of an arc is 95°. What is the measure
of an inscribed angle that intercepts it?
A. 47.5°
B. 95°
C. 190°
D. 265°