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GEOMETRY CHAPTER 10 PRACTICE TEST
- Identify all chords for circle O.
A
B
C
F
O
E
D
G
H
- Identify all tangents for circle O.
A
B
C
F
O
E
D
G
H
- A circle is the set of all points in a plane that _____.
[A] have a center
[B] are equidistant from a given point
[C] have a diameter
[D] lie within a given radius
- Define a secant of a circle and illustrate the
definition on the circle below.
- (^) AB is tangent to O at A (not drawn to scale). Find the length of the radius r , to the nearest tenth.
A
O
B
r
- Give the center and radius of circle A and circle B. Describe the intersection of the two circles and describe all common tangents.
x
y
–10 10
10
A
B
- Given: (^) ST is tangent to R at S Find RT.
- Find m PQ
in A. Drawing is not to scale.
y + °
b 45 g
A
2 y − 15
°
b g
Q
S
P
R
- Given: In O, m (^) BAC = 294 (^) °. Find m (^) ∠ A.
GEOMETRY CHAPTER 10 PRACTICE TEST
A
O
C
B
[A] 33 °
[B] 27 °
[C] 16.5 °
[D] 13.5 °
- Identify the minor congruent arcs in the figure.
A
B
C
D
E F
G
60 °
35 ° 45 ° 70 °
25 ° (^70) °
55 °
- Given circle O with radius 34 and OC = 16.
Find the measure of (^) AB.
O
A C B
- Find the value of x.
x
[A] 16.
[B] 8.
[C] 9.
[D] 15.
- Given: P and (^) PT ⊥ to chord (^) RS at T. Decide whether or not RT = TS. Explain your reasoning.
- Find m (^) ∠ PSQ if m (^) ∠ PSQ = (^3) y − 10 and m (^) ∠ PRQ = (^2) y + 10.
Q
S
P
R
[A] 10 °
[B] 25 °
[C] 20 °
GEOMETRY CHAPTER 10 PRACTICE TEST
m ∠ 1 = 83 ° , m ∠ 2 = 86 ° , m ∠ 3 = 94 ° , m ∠ 4 = 97 °
[B]
m ∠ 1 = 86 ° , m ∠ 2 = 83 ° , m ∠ 3 = 94 ° , m ∠ 4 = 97 °
[C]
m ∠ 1 = 83 ° , m ∠ 2 = 86 ° , m ∠ 3 = 97 ° , m ∠ 4 = 94 °
[D]
m ∠ 1 = 86 ° , m ∠ 2 = 83 ° , m ∠ 3 = 97 ° , m ∠ 4 = 94 °
- In the figure shown (not drawn to scale),
mBCD = 112 ° , mDEF = 98 ° , mFGH = 130 °,
and (^) mHAB = 20 ° .Find m (^) ∠ FPD.
P
G
A
H F
C
D
B
• E
[A] 20 °
[B] 39 °
[C] 16 °
[D] 92 °
- Find the measure of (^) ∠ 1.
- Find the diameter of the circle. (^) BC = 11, and
DC = 22. Round your answer to the nearest tenth.
O
A
B
D C
[A] 35.
[B] 33.
[C] 16.
[D] 55.
- Find the equation of the circle of radius 3 with its center at the origin.
- Find the equation of the circle with center (5, –
- and radius of 2.
- Find the length of the leg of this right triangle. LEAVE ANSWER IN SIMPLIFIED RADICAL FORM.
a
7
9
- Find the altitude of an isosceles triangle with base 10 and congruent sides of length 9.
- Given: Rectangle PQRS with QR = 8 and SQ =
- What is the value of y?
- Find the area of this right triangle if (^) b = 10 and c = 2 41.
GEOMETRY CHAPTER 10 PRACTICE TEST
a
b
c
- A set of Pythagorean triples is _____.
[A] 1, 1, 2
[B] 3, 5, 9
[C] 6, 9, 12
[D] 5, 12, 13
- Which set of lengths cannot form a right triangle?
[A] 4 mm, 7.5 mm, 8.5 mm
[B] 8 mm, 15 mm, 17 mm
[C] 16 mm, 30 mm, 34 mm
[D] 9 mm, 15 mm, 17 mm
- A triangle has side lengths of 6, 9, and 11. Decide whether it is an acute, right, or obtuse triangle. Explain.
- Write the ratio of side lengths to hypotenuse in a 45-45-90 right triangle.
- Write the ratio of side lengths to the hypotenuse in a 30-60-90 right triangle.
- What is the length of the diagonal of a square
with side lengths 7 2?
- Find the value of x and y.
60°
x y
20
- Find the value of (^) x and (^) y.
30°
7
x
y
- Find the value of x , to the nearest whole number. (not drawn to scale) A
C B
28°
x 8
39. Solve the right triangle: α = 40 ° and a = 17;
find β , b , and c
c
a
b β
α
- To find the height of a tower, a surveyor positions a transit that is 2 m tall at a spot 55 m from the base of the tower. She measures the angle of elevation to the top of the tower to be 51 (^) °. What is the height of the tower, to the nearest meter?
GEOMETRY CHAPTER 10 PRACTICE TEST
Reference: [10.4.1.62] [22] 70°
Reference: [10.5.2.79] [23] [B]
Reference: [10.6.1.81] [24] (^) x^2 + y^2 = 9
Reference: [10.6.1.82]
[25] x − 5 + y + 2 = 4 2 2 b g b g
Reference: [9.2.2.9a] [26] 4 / 2
Reference: [9.2.2.16]
[27] 56 or 2 14
Reference: [9.2.2.17] [28] 6
Reference: [9.2.2.23] [29] 40
Reference: [9.2.2.25] [30] [D]
Reference: [9.3.1.29] [31] [D]
Reference: [9.3.2.32] [32] Since (^6 2) + 9 2 < 112 , it is an obtuse triangle.
Reference: [9.3.2.34a]
[33] 1:1: 2
Reference: [9.3.2.34b] [34] 1:1 3 :
Reference: [9.4.1.42] [35] 14
Reference: [9.4.1.46] [36] x = 10, y = (^10 )
Reference: [9.4.1.45] [37] (^) x = 7 3 , y = 14
Reference: [9.6.1.77] [38] 17
Reference: [9.6.1.83] [39] β = ° ≈ ≈
b c
Reference: [9.5.2.72] [40] 70 m
