Geometry
Name_________________________
Unit 10 Day 4
WARM UP
Line t is tangent to the circle. Find the values of x and y.
1.
2.
36
230
x
x
t
68
3.
4.
y
22
72
y
135
x
27
Today we will understand properties of chords
And
By the end of class today, you will be able to find segment lengths in circles
Notes
Applying Properties of Chords & Finding Segment Lengths in Circles
Theorem –
In the same circle or in congruent circles, two minor arcs are congruent iff
their corresponding chords are congruent.
Bisecting Arcs
If XY  YZ, then the point Y, and any line, segment, or ray that contains Y, bisects XYZ.
Examples
1. Use the diagram of circle D.
a. If AB = 110°, find BC.
B
9
A
D
9
b. If AC = 150°, find AB.
C
Theorem –
If one chord is a perpendicular bisector of another chord, then the first chord
is a diameter.
If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.
C
2. Use the diagram of circle E to find the length of AC.
E
B
F
D
7
A
3. Find the measure of the indicated arc in the diagram.
a. CD
B
C
A
b. DE
9x
c. CE
D
E
(80 - x)
Theorem –
In the same circle or in congruent circles, two chords are congruent iff they
are equidistant from the center.
4. In the diagram of circle C, QR = ST = 16. Find CU.
Q
16
R
U
S
2x
C
16
V
T
5x - 9
C
Theorem –
̅̅̅̅
𝑨𝑬 ∙ ̅̅̅̅
𝑬𝑩 = ̅̅̅̅
𝑪𝑬 ∙ ̅̅̅̅
𝑬𝑫
B
E
A
D
Theorem –
̅̅̅̅ ∙ ̅̅̅̅̅̅
̅̅̅̅ ∙ 𝑬𝑩
̅̅̅̅ = 𝑬𝑪
𝑬𝑨
𝑬𝑫
B
A
E
C
A
Theorem –
𝟐
̅̅̅̅ ∙ 𝑬𝑫
̅̅̅̅ = 𝑬𝑨
̅̅̅̅
𝑬𝑪
E
C
D
D