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Geometry
Mr. Schopper
Chapter 6 - RETEST
Name ______________________ section ____
Properties of Circles
Read each of the following statements very carefully.
Just one word could change its meaning.
Then, identify the statement as true or false.
Place a T in the  if the statement is true. Place an F in the  if the statement
is false and then change the underlined word or phrase to make it true.

1.
A circle is a set of points in space at a given distance from a given point.

2.
A diameter is a segment connecting any point on the circle and the center point.

3.
A chord is a segment connecting any two points on a circle.

4.
A secant is a line, in the plane of a circle, that intersects the circle in exactly one point.

5.
The measure of a secant-tangent angle is equal to twice the measure of its intercepted arc.

6.
Two circles are congruent if they have the same center.

7.
The ratio of a circle’s diameter to circumference is better known as

8.
The opposite angles of a cyclic quadrilateral are congruent.
.
.
Fill in the blank with a word or phrase to make each of the following statements true.
9.
A tangent segment to a circle, at the point of tangency, is ________________________ to the
radius at the point of tangency.
10.
Every angle inscribed in a semicircle is a(n) ____________________ .
11.
The length of an arc is equal to the ________________ of the arc divided by 360°,
times the _____________________ of the circle.
12.
The radius of a circle drawn perpendicular to a chord will ________________ the chord.
Answer each of the following. Show your work to receive full credit.
R
13.
The chords RS and ST are congruent.
Find m RS .
T
54
S
14.
E
Find the m EH in the figure to the right.
AE is tangent to C
C
H
15
S
A
15.
In the figure below, DM is a diameter of the circle.
DM  CR at point P and m CR = 138.
m CP = x2 - 14
and
m PR = 2x + 21
R
D
a. Find the numerical value of x.
P
C
M
b. Now, find m CR.
c. Find m RM.
16.
Find the numerical value of x in each figure below.
32
a.
b.
141
29
x
59
S
N
x
17.
The inscribed quadrilateral, QUAD, is called a(n) ____________
quadrilateral. Use the information in the figure below to answer the
following questions.
D
a.
m  ADQ = ______
101
Q
b.
m QD = ______
D
65
A
92
c.
m AU = ______
d.
m  DQU = ______
e.
m  DAU = ______
f.
If the radius of
U
D is 18 cm, find the length of QU.
18.
Find m MAJ in the figure below where PM and PJ are tangent to
Show your work.
M
P
42
C
A
J
C.
19.
In the figure to the right, DI is a diameter.
Find the indicated measures.
124
a.
m  W = ______
I
W
32
20.
b.
m WD = ______
c.
m  WED = ______
d.
m DE = ______
e.
m AE = ______
C
D
A
48
E
Jewel Case has signed up to take a spinning class at her local fitness center.
Her bike has a 24 inch diameter wheel.
a.
To the nearest inch, what is the circumference
of the wheel ?
b.
She is able to bike at an average speed of 6 mph for 10 minutes.
To the nearest revolution, how many revolutions does her bike’s wheel make
in the 10 minutes she was spinning ?