Math 083 Sample Exam 3 A Given:

Math 083
Sample Exam 3
____
1.
Given:
Prove:
____
ABC right at A and DA
ADC ~ DBA
A
BC .
C
D
B
C
2.
Given:
Prove:
at C
ABC right
2
2
b
2
a + b = c
a
A
c
B
3.
The chords AB and CD intersect at point E, and DQ and FG
are tangent to the circle.
AD = 5 and m ADQ
a.
m ADC
b.
m AFC
c.
m AEC
d.
m BC
e.
FG
40 0 .
92 0 , DB 580 , FD = 4,
If the arc AC
Find
Q
G
4. Park rangers catch, tag, and then release 50 deer back into a
wildlife refuge. Two months later they selected a sample of 108
deer, and they found out that 25 were tagged. Approximately how
many deer are in the refuge?
5. Construct a tangent line to a circle from a point P on the
circle.
P
O
6.
CD bisects
Find AD
ACB so that AC = 8, CB = 15, and DB = 12
D
B
A
C
7. AB is a chord of the circle Q with AB = 16. Radius QC is
perpendicular to AB at D. If QC = 10, find QD.
___
8.
Given:
___
BA , BC are tangent to circle O at A and C
D is midpoint of AC
Find:
1
2
A
O
D
C
1
2
B
D
____
9.
Given:
Prove:
C
____
DC || AB
I
AI DI CI BI
B
A
10.
Given:
Prove:
AP is the tangent line
AP 2
PB PC
A
P
B
C
11) Complete each statement
a) An angle inscribed in a semicircle is ______ angle.
b) Two tangent segments to circle from an external point are __________.
c) The length of the altitude to the hypotenuse of a right triangle is the geometric mean of
the lengths of the_____________ of the ___________.
d) In a circle, congruent chords have congruent __________.
e) If two ________ angles of a circle intercept the same arc, then they are congruent.
f) The tangent line is ________to the radius at the tangent point.
g) If a ray bisects one angle of a triangle, the it divides the opposite side into ______
whose lengths are proportional to the lengths of _____ _____ that formed bisected angle.