AnswersMathematics IICircles With and Without Coordinates

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Statements Reasons 1. circle cap o ; angle cap A intercepts overarc BC ; angle cap d intercepts overarc BC 1. given 2. m angle cap A is equal to 1 half times open paren m overarc BC close paren 2. ? 3. m angle cap d is equal to 1 half times open paren m overarc BC close paren 3. ? 4. m angle cap A is equal to m angle cap d 4. substitution property 5. angle cap A is congruent to angle cap d 5. definition of congruent angles Two statements are missing reasons. What reason can be used to justify both statements 2 and 3 ?

A
central angle of a triangle has the same measure as its intercepted arc.
B
inscribed angles theorem
C
angle formed by a tangent and a chord is half the measure of the intercepted arc.
D
third corollary to the inscribed angles theorem
2
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What is the measure of angle CDF ?

A
19 degrees
B
26 degrees
C
14 degrees
D
38 degrees
3

In circle cap y , what is m frown set over TU ?

A
106 degrees
B
82 degrees
C
118 degrees
D
100 degrees
4

What is the approximate length of the radius, r ?

A
28 point 3 cm
B
4 point 5 cm
C
9 point 0 cm
D
14 point 2 cm
5

What is the measure of angle ADM ?

A
30.0 degrees
B
45.0 degrees
C
22.5 degrees
D
67.5 degrees
6

What are the measures of angles cap m and cap n ?

A
m angle cap m is equal to 61 degrees and m angle cap n is equal to 113 degrees
B
m angle cap m is equal to 119 degrees and m angle cap n is equal to 67 degrees
C
m angle cap m is equal to 113 degrees and m angle cap n is equal to 61 degrees
D
m angle cap m is equal to 67 degrees and m angle cap n is equal to 119 degrees
7

m angle DFE is equal to 80 degrees What is the measure of arc overarc GH ? [Blank 1] degree

Answer:

80

8

What is the measure of overarc BC ?

A
160 degrees
B
100 degrees
C
120 degrees
D
130 degrees
9

Which statements about the clock are accurate? Choose three correct answers.

A
The length of the minor arc between 6 and 7 is approximately 5 point 2 inches.
B
The circumference of the clock is approximately 62 point 8 inches.
C
The minor arc measure when one hand points at 12 and the other hand points at 4 is 120 degrees .
D
The central angle formed when one hand points at 1 and the other hand points at 3 is 30 degrees .
E
The length of the major arc between 3 and 10 is approximately 31 point 4 inches.
10

What is the center of a circle represented by the equation open paren x minus 5 close paren squared plus open paren y plus 6 close paren squared is equal to 4 squared ?

A
6 comma negative 5
B
5 comma negative 6
C
negative 6 comma 5
D
negative 5 comma 6
11

A parabola has a vertex at the origin. The focus of the parabola is located at open paren negative 2 comma 0 close paren Which is the equation for the directrix related to the parabola?

A
x is equal to 2
B
y is equal to 2
C
y is equal to negative 2
D
x is equal to negative 2
12

Liliana is making a vase with a circular base. She wants the area of the base to be between 135 cm squared and 155 cm squared Which circle could represent the base of the vase? Use 3 point 1 4 for pi

A
Image with description A circle has a radius labeled 6 centimeters.
B
Image with description A circle has a radius labeled 7 centimeters.
C
Image with description A circle has a radius labeled 8 centimeters.
D
Image with description A circle has a radius labeled 9 centimeters.
13

Two chords intersect at a point inside a circle that is not the center of the circle. Which statement must be true?

A
The sum of the measures of each pair of vertical angles is equal to the sum of the measures of the intercepted arcs.
B
The measures of each pair of opposite arcs sum to 180 degrees .
C
Each arc measure is equal to one-half the sum of the vertical angles that intercept the arc.
D
Each angle measure is equal to the measure of the arc it intercepts.
14

What is the radius of a circle whose equation is open paren x minus 7 close paren squared plus open paren y minus 10 close paren squared is equal to 4 ?

A
8 units
B
4 units
C
2 units
D
16 units
15

Which circle shows overarc AB that measures 60 degrees ?

A
Image with description Circle with center O has points A and B on the circle and another unlabeled point on the left side of the circle. Segments from the unlabeled point to A and B form an angle labeled 60 degrees.
B
Image with description Circle with center O has points A and B on the circle. Segment A B is drawn. A tangent line touches the circle at A, and the angle between the tangent line and segment A B is labeled 60 degrees.
C
Image with description Circle with center O has points A and B on the circle. Segments O A and O B are drawn, forming a central angle labeled 60 degrees.
D
Image with description Circle with center O has points A, B, and Y on the circle. Segment B Y passes through O, and segment A Y is drawn. The angle at Y between segments Y A and Y B is labeled 60 degrees.
16

Which circle has a central angle that measures 40 degrees ?

A
Image with description Circle with center U has points V and Z on the circle. Segments U V and U Z are drawn. The angle formed by segments U V and U Z at point U is labeled 40 degrees.
B
Image with description Circle with center U has points Z and V on the circle and point X outside the circle. A line passes through points X and Z. Segment Z V connects points Z and V. The angle formed by ray Z X and segment Z V is labeled 40 degrees.
C
Image with description Circle with center U has points X, V, and Z on the circle. Segments X V and X Z are drawn. The angle formed by segments X V and X Z at point X is labeled 40 degrees.
D
Image with description Circle with center U has points V, X, and Z on the circle. Segments X V and X Z are drawn. The angle formed by segments X V and X Z at point X is labeled 40 degrees.
17

A circular table top has a radius of 24 inches. What is the area of the table top, to the nearest square inch? Use 3 point 1 4 for pi

A
75 in. squared
B
7235 in.2
C
1809 in. squared
D
151 in. squared
18

What are the coordinates of the focus of the parabola?

A
open paren 0 comma negative 2 close paren
B
open paren 0 comma 2 close paren
C
open paren 2 comma 0 close paren
D
open paren negative 2 comma 0 close paren

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