Name: _________________________________________________
Date: __________
Teacher: ________________________________________________
Unit 12 - Review 3
1. For each of the following, fill in the formula (if any)that you would use to find the angle.
Then find the measure of angle x.
Formula:
Formula:
Formula:
Formula:
x=
x=
x=
x=
x
Formula:
Formula:
Formula:
Formula:
x=
x=
x=
x=
2. Fill in the following theorems:
 Two chords of a circle are congruent if and only if _______________________________________.
 If two parallel lines intersect a circle, ___________________________________________________.
 If an angle is _____________________________________________________ then it is a right angle.
 If a diameter/radius is perpendicular to a chord, then ___________________________________.
 A line is tangent to a circle if and only if ________________________________________________
____________________________________________________________________________________
 If two tangents of a circle _______________________________________, then they are congruent.
 If two inscribed angles _________________________________________, then they are congruent.
 All radii of ____________________________________________________________ are congruent.
3. In the diagram of circle O, m  AOC
= 52. Find m  ABC.
9. In the accompanying diagram of a
circle,
is a diameter and m
Find m  CBA.
C
O
C
=50.
A
B
B
A
4. If the diagram of circle O, XA and
10. In the accompanying diagram of circle
O, chords
XB are tangents and m  XAB =
75. Find m  AXB.
A
and
intersect at E
and
is a diameter. If m
find m  AED.
X
= 82,
C
B
E
O
D
A
B
O
5. In the accompanying diagram, ABC is
inscribed in circle O and
is a
diameter. Find the m  ACB
C
A
11. In the accompanying diagram of a
B
circle, chords
and
intersect at
E and the ratio of the measures of
AC : CB : BD : DA is 4:2:6:8. Find m  AEC.
O
6. In the accompanying diagram of a
circle, chords
C
E
B
and
E. If m
= 75, and m
m  AED.
intersect at
= 45, find
E
7.
In the accompanying diagram,
12. In the accompanying diagram of circle
O, m  ACB = 38. Find m  AOB.
segments
,
and
are tangent
to circle O at A, B and C, respectively.
If SB = 3, BT = 5 and TR = 13, what is
the measure of RS?
S
B
O
A
B
O
R
C
8. In the accompanying diagram of a
A
E
D
and
C circle, chords
E, m
= 50, and m
 AED.
B
D
A
D
A
B
C
intersect at
= 150. Find m
A
13. In the accompanying diagram, secant
T
intersects circle O at D, secant
intersects circle O at E, AE = 4, AC =
24, AB = 16. Find AD.
C
14. In the accompanying diagram,
and
are tangents drawn to circle O and chord
is drawn. If m  P = 40, what is m  PQS?
18. In the accompanying diagram, chord
parallel to diameter
. If
is
, what is
?
Q
P
O
S
19. If EC = 25 and CG = 9, find the length of CF.
15. In the diagram below of circle O, radius
is 5
cm. Chord
is 8 cm and is perpendicular to
at point P. What is the length of
, in
centimeters?
20.
16. In the accompanying diagram of circle O, m
= 150. Find m  ABC
A
O
21. How many common tangents can be
drawn for each diagram?
C
B
17. In the accompanying diagram of circle O, chords
and
are drawn,
is a diameter,
, and
. Find
.
22.
In the accompanying diagram of circle O,
is a chord, AO = 8, and the ratio of the measures of
Find:
a) m
is a diameter,
:
:
:
is a tangent,
is a secant.
= 3:2:1:4.
A
b) m  P
O
D
E
C
B
c) m  BEC
d) m  BAE
P
e) m  PBE
23. for finding the segments (i.e. (AB)(BC) = (ED)(EF) ).
Formula:
24. DE= 12, ME= 5, NE =
6, find FN.
Formula:
25. KR= 9, KQ =4, Find
RS.
Formula:
26. If QB = x, SB = 6, BT =
4, and BR = x + 5,
Find BR.