Question 1

In a circle with center

O

, points

A

,

B

,

C

, and

D

lie on the circumference in order such that

ABCD

is a cyclic quadrilateral. If the measure of angle

\angle ABC = 105^{\circ}

and the measure of angle

\angle CAD = 40^{\circ}

, what is the measure of angle

\angle ACD

?

Accepted Answer

35 degrees

Answer

40 degrees

Answer

65 degrees

Answer

75 degrees

Question 2

A circle has a radius of

O

cm. If a sector of this circle has an arc length of

A

cm, what is the area of this sector?

Accepted Answer

12\pi

square cm

Answer

12\pi

square cm

Answer

12\pi

square cm

Answer

12\pi

square cm

Question 3

In a circle with center

O

, a tangent

A

is drawn from an external point

B

to point

C

on the circle. If

D

cm and the radius of the circle is

ABCD

cm, what is the distance from point

\angle ABC = 105^{\circ}

to the center

\angle CAD = 40^{\circ}

?

Accepted Answer

13 cm

Answer

17 cm

Answer

7 cm

Answer

<math>\sqrt{119}</math> cm

Question 4

In a circle with center

O

, chord

A

and chord

B

intersect at point

C

inside the circle. If

D

,

ABCD

, and

\angle ABC = 105^{\circ}

, what is the length of segment

\angle CAD = 40^{\circ}

?

Accepted Answer

12

Answer

3

Answer

10

Answer

14

Question 5

In a circle with center

O

, a central angle

A

measures

B

. If point

C

lies on the major arc

D

, what is the measure of the inscribed angle

ABCD

?

Accepted Answer

44 degrees

Answer

88 degrees

Answer

22 degrees

Answer

176 degrees

Question 6

In a circle, a chord of length

O

cm is at a distance of

A

cm from the center

B

. What is the length of the diameter of the circle?

Accepted Answer

20 cm

Answer

24 cm

Answer

12 cm

Answer

10 cm

Question 7

Two tangents

O

and

A

are drawn to a circle with center

B

from an external point

C

. If the angle between the two tangents

D

is

ABCD

, what is the measure of the minor arc

\angle ABC = 105^{\circ}

?

Accepted Answer

110 degrees

Answer

250 degrees

Answer

70 degrees

Answer

140 degrees

Question 8

In a circle with center

O

, chord

A

is equal to the radius of the circle. What is the measure of the inscribed angle

B

, where

C

is a point on the major arc

D

?

Accepted Answer

30 degrees

Answer

90 degrees

Answer

45 degrees

Answer

60 degrees

Question 9

In a cyclic quadrilateral

O

, the measure of

A

is

B

and the measure of the opposite angle

C

is

D

. What is the value of

ABCD

in degrees?

Accepted Answer

100 degrees

Answer

30 degrees

Answer

80 degrees

Answer

70 degrees

Question 10

In a circle with center

O

, chord

A

is produced to a point

B

outside the circle. A tangent

C

is drawn from

D

to point

ABCD

on the circle. If

\angle ABC = 105^{\circ}

and

\angle CAD = 40^{\circ}

, what is the length of chord

\angle ACD

?

Accepted Answer

5

Answer

2

Answer

9

Answer

13

Question 11

In a circle with center

O

, points

A

,

B

,

C

, and

D

lie on the circumference in order to form a cyclic quadrilateral. If the measure of diagonal angle

ABCD

and

\angle ABC = 105^{\circ}

, what is the measure of

\angle CAD = 40^{\circ}

?

Accepted Answer

75^{\circ}

Answer

95^{\circ}

Answer

105^{\circ}

Answer

180^{\circ}

Question 12

A circle has a radius of

O

cm. A sector is formed by an arc with a central angle of

A

. What is the area of this sector in terms of

B

?

Accepted Answer

6\pi	ext{ cm}^2

Answer

3\pi	ext{ cm}^2

Answer

12\pi	ext{ cm}^2

Answer

36\pi	ext{ cm}^2

Question 13

In a circle with center

O

, a tangent line is drawn from an external point

A

to touch the circle at point

B

. If the radius of the circle is

C

units and the distance from the center

D

to point

ABCD

is

\angle ABC = 105^{\circ}

units, what is the length of the tangent segment

\angle CAD = 40^{\circ}

?

Accepted Answer

12

Answer

14.4

Answer

8

Answer

\sqrt{194}

Question 14

An inscribed angle

O

subtends an arc

A

that measures

B

. What is the measure of the angle

C

?

Accepted Answer

55^{\circ}

Answer

110^{\circ}

Answer

220^{\circ}

Answer

70^{\circ}

Question 15

In a circle with center

O

, chord

A

and chord

B

intersect at point

C

inside the circle. If

D

cm,

ABCD

cm, and

\angle ABC = 105^{\circ}

cm, what is the length of segment

\angle CAD = 40^{\circ}

?

Accepted Answer

6	ext{ cm}

Answer

4	ext{ cm}

Answer

13.5	ext{ cm}

Answer

9	ext{ cm}

Question 16

In a circle with center

O

, chord

A

is equal in length to the radius of the circle. What is the measure of the minor arc

B

?

Accepted Answer

60^{\circ}

Answer

120^{\circ}

Answer

90^{\circ}

Answer

30^{\circ}

Question 17

Two tangents

O

and

A

are drawn to a circle with center

B

from an external point

C

. If the angle between the two tangents

D

is

ABCD

, what is the measure of the central angle

\angle ABC = 105^{\circ}

?

Accepted Answer

110^{\circ}

Answer

70^{\circ}

Answer

140^{\circ}

Answer

90^{\circ}

Question 18

In a circle with center

O

, chord

A

is

B

units long. If the perpendicular distance from the center

C

to the chord is

D

units, what is the length of the radius of the circle?

Accepted Answer

10

Answer

20

Answer

\sqrt{52}

Answer

8

Question 19

In a circle with center

O

, tangent

A

touches the circle at point

B

. A chord

C

is drawn such that the angle between the tangent and the chord,

D

, is

ABCD

. If

\angle ABC = 105^{\circ}

is a point on the major arc

\angle CAD = 40^{\circ}

, what is the measure of the inscribed angle

\angle ACD

?

Accepted Answer

50^{\circ}

Answer

40^{\circ}

Answer

100^{\circ}

Answer

25^{\circ}

Question 20

In a circle with center

O

, chord

A

and chord

B

are equal in length. If the measure of arc

C

is

D

and the angle

ABCD

is subtended by chord

\angle ABC = 105^{\circ}

at the center, what is the measure of angle

\angle CAD = 40^{\circ}

?

Accepted Answer

80^{\circ}

Answer

40^{\circ}

Answer

160^{\circ}

Answer

100^{\circ}

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