Student’s Name Student ID No. Address
Geometry Lesson 5 Examination
Please read these instructions before you begin to answer the questions that follow.
Write your answers and your work on this examination. When you are satisfied that your answers are correct, write them on the Answer Sheet found right after the exam. Then send the Answer Sheet only (not the exam itself) to The Keystone School for grading. Attach separate paper for your work if necessary. Good Luck!
In K, m HKG = x + 10 and m IKJ = 3x – 22. Find .
Answer: ______________________
State the coordinates of the center and the measure of the radius.
x2 + y2 – 4 = 0
Answer: ______________________
Use G with and
Use G with andtangent at A and E for questions 3-5.
Find ACE.
Answer: ______________________
Find ADB.
Answer: ______________________
Find AFE.
Answer: ______________________
Find the length of in R to the nearest hundredth.
a.
4.71 m
b.
9.42 m
c.
1.57 m
d.
3.14 m
The diameter of C is 18 units long. Find the length of an arc that has a measure of 100. Round to the nearest hundredth.
Answer: ______________________
The wheels on Elliot’s truck each have a circumference of 22 inches. Determine the radius of each wheel to the nearest tenth.
a.
7 in.
b.
3.5 in.
c.
5 in.
d.
2.5 in.
Use X for questions 9-12.
Name a tangent.
a.
b.
c.
d.
Name a radius.
a.
b.
c.
d.
Name a chord.
a.
b.
c.
d.
If is tangent to C at A, find BC.
a.
24 in.
b.
in.
c.
6 in.
d.
in.
Find x if is tangent to P at A. Answer: ______________________
Find x. Answer: ______________________
Find ABC.
a.
70
b.
90
c.
50
d.
140
Find the center of the circle whose equation is (x + 11)2 + ( y – 7)2 = 121.
a.
(121, 49)
b.
(11, –7)
c.
(–11, 7)
d.
11
Find AF.
a.
11.25
b.
10
c.
7.5
d.
4
Find x.
Answer: ______________________
Find x.
a.
122
b.
61
c.
68
d.
95
Find x.
a.
29
b.
122
c.
58
d.
61
, , , and are tangent to X. Find RS.
a.
cannot tell
b.
9 in.
c.
13 in.
d.
12 in.
Find ZC.
a.
16
b.
22
c.
32
d.
4
Identify the graph of (x – 3)2 + ( y + 2)2 = 4.
a.
b.
c.
d.
Find each measure.
Answer: ______________________
Answer: ______________________
Write the equation of a circle with a diameter having endpoints at (–2, 6) and (8, 4).
Answer: ______________________
In A, CG = 5x + 2 and GD = 7x – 12. Find x.
Answer: ______________________
Find .
a.
66
b.
21
c.
45
d.
57
Find x.
a.
204
b.
102
c.
78
d.
90
Find YB if the diameter of A is 10 inches, the diameter of B is 8 inches, and AX = 3 inches.
Answer: ______________________
In O, PQ = 18 meters. Find the distance from O to .
Answer: ______________________
Use D for question 32..
Name a chord that is not a diameter.
a.
b.
c.
d.
Find .
a.
48
b.
80
c.
64
d.
40
Write the equation of each circle.
center at (0, 0), diameter 18
Answer: ______________________
center at (–3, –3), passes through (–2, 3)
Answer: ______________________
center at (–7, 11), radius 8
Answer: ______________________
EFGH is a quadrilateral inscribed in P with E = 72 and F = 49. Find H.
a.
131
b.
57
c.
90
d.
108
Find the radius and diameter of a flying disc with a circumference of π inches.
Answer: ______________________
Write the equation of a circle with a radius of length 10 and a center at (–4, –9).
Answer: ______________________
Points X and Y lie on P so that PX = 5 meters and m XPY = 90. Find the length of to the nearest hundredth.
a.
3.93 m
b.
15.71 m
c.
7.85 m
d.
19.63 m
A regular decagon is inscribed in a circle. Find the measure of each minor arc.
Answer: ______________________
Determine the length of the radius of a circle with an equation of (x – 3)2 + ( y – 2)2 = r2 and containing (1, 4).
Answer: ______________________
Triangle DEF is circumscribed about O with DE = 15 units, DF = 12 units, and EF = 13 units. The length of the segment from E to the point of tangency on EF is 8. Find the length of each segment whose endpoints are D and the points of tangency on and .
Answer: ______________________
is tangent to Z at (1, 7). If Z has coordinates (5, 2), find the slope of .
Answer: ______________________
Find the equation of a circle with center (0, 0) and radius 4.
a.
x2 + y2 = 4
b.
(x – 4)2 + ( y – 4)2 = 16
c.
x2 + y2 = 16
d.
4x + 4y = 16
Find the equation of P.
a.
(x – 3)2 + y2 = 4
b.
x2 + ( y – 3)2 = 2
c.
x2 + ( y – 3)2 = 4
d.
(x – 3)2 + y2 = 2
Find the radius of a circle if a 48-meter chord is 7 meters from the center.
a.
25 m
b.
41 m
c.
24 m
d.
14 m
Find .
a.
58
b.
28
c.
56
d.
76
Chords and are equidistant from the center of O. If XY = 2x + 30 and WV = 5x – 12, find x.
a.
14
b.
6
c.
28
d.
58
50. Graph (x + 1)2 + ( y – 2)2 = 16.
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