Chapter 10-5
Tangents
• Use properties of tangents.
• tangent
• Solve problems involving
circumscribed polygons.
• point of tangency
Standard 7.0 Students prove and use theorems
involving the properties of parallel lines cut by a
transversal, the properties of quadrilaterals, and the
properties of circles. (Key)
Standard 21.0 Students prove and solve problems
regarding relationships among chords, secants,
tangents, inscribed angles, and inscribed and
circumscribed polygons of circles. (Key)
Reminder

Tangent—a line that intersects the
circle in only one point
Secant
Radius
Chord
Tangent Theorem
A
line is tangent to a circle  it is  to
a radius at its endpoint on the circle
Examples:
Find Lengths
Because y is the length of the diameter, ignore the
negative result. Thus, y is twice QR or y = 2(12) = 24.
A. 15
B. 20
C. 10
D. 5
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Identify Tangents
Because the converse of the
Pythagorean Theorem did not
prove true in this case, ΔABC is
not a right triangle.
Identify Tangents
First determine whether ΔEWD
is a right triangle by using the
converse of the Pythagorean
Theorem.
Because the converse of the Pythagorean Theorem is
true, ΔEWD is a right triangle and EWD is a right angle.
A. yes
B. no
A
B
C
0%
C
0%
B
0%
A
C. cannot be
determined
1.
2.
3.
A. yes
B. no
0%
0%
C
0%
A
B
C
B
1.
2.
3.
A
C. cannot be
determined
12
r
r
10
r2 + 122 = (r + 10)2
r2 + 144 = r2 + 20r + 100
144 = 20r + 100
44 = 20r
44 11
r= 
20 5

If two segments from the same external
point are tangent to a circle  they are 
C
AC = AB
A
B
Congruent Tangents
ALGEBRA Find x. Assume
that segments that appear
tangent to circles are tangent.
Congruent Tangents
Use the value of y to find x.
10
Answer: 1
10
ALGEBRA Find a. Assume that segments that
appear tangent to circles are tangent.
A. 6
0%
B. 4
C. 30
D. –6
1.
2.
3.
4.
A
A
B
C
D
B
C
D
Triangles Circumscribed About a Circle
Interactive Lab: Tangents and
Communication Signals
16
45
18
16 + 29 = 45
P = 16 + 18 + 18 + 45 + 45 + 16 = 158
A. 86
B. 180
0%
D
A
D. 162
A
B
0%
C
D
C
0%
A.
B.
0%
C.
D.
B
C. 172
Homework
Ch 10-5
Pg 593
5 – 22, 30,
31, 43 – 46