Question 1

In the diagram, chord AB intersects chord CD at E,
DE = 2x + 8, EC = 3, AE = 4x − 3, and EB = 4. The value of x is

Accepted Answer

3.6

Answer

5

Answer

1

Answer

10.25

Question 2

In the diagram, f CE = 10, ED = 6, and AE = 4, what is the length of EB?

Accepted Answer

15

Answer

12

Answer

2.4

Answer

6.7

Question 3

In the diagram of △PAO, AP is tangent to circle O at point A, OB = 7, and BP = 18.  The length of PA is

Accepted Answer

24

Answer

17

Answer

12

Answer

10

Question 4

In the diagram, diameter AB is perpendicular to chord CD at E, OA = 6, and OE = 2.  The length of CE is

Accepted Answer

4$\sqrt{2}$

Answer

8$\sqrt{2}$

Answer

2$\sqrt{3}$

Answer

4$\sqrt{3}$

Question 5

In the diagram, tangents AC and AD are drawn.  What is the length of BD?

Accepted Answer

9

Answer

18

Answer

5.5

Answer

12

Question 6

In a circle, chords AB and CD intersect at point E.  If AE = 8, AB = 20, and DE = 16, what is the length of CE?

Accepted Answer

6

Answer

10

Answer

9

Answer

12

Question 7

In the diagram, AB $\perp$ CD.  Which statement is always true?

Accepted Answer

$\widehat{CB}$ $\cong$ $\widehat{DB}$

Answer

$\widehat{CB}$ $\cong$ $\widehat{CA}$

Answer

$\widehat{CA}$ $\cong$ $\widehat{DB}$

Answer

$\widehat{CB}$ $\cong$ $\widehat{DA}$

Question 8

In the diagram, circle O has a radius of 5, and CE = 2. Diameter AC is perpendicular to chord BD at E.  The length of BD is

Accepted Answer

8

Answer

12

Answer

4

Answer

10

Question 9

In the diagram, PS is a tangent to circle O at point S, PQR is a secant, PS = x, PQ = 3, and PR = x + 18.  The length of PS is

Accepted Answer

6

Answer

3

Answer

12

Answer

9

Question 10

In the diagram, tangent PA and secant PBC are drawn to circle O from external point P.  If PB = 4 and BC = 5, what is the length of PA?

Accepted Answer

6

Answer

20

Answer

8

Answer

9

Question 11

In the diagram, AB, BC, and AC are tangents, AF = 6, CD = 5, and BE = 4.  What is the perimeter of △ABC?

Accepted Answer

30

Answer

15

Answer

25

Answer

60

Question 12

In the diagram of circle O, radius OC is 5. Chord AB is 8 and is perpendicular to OC at point P.  The length of OP is

Accepted Answer

3

Answer

8

Answer

4

Answer

2

Question 13

In the diagram,  ABC is circumscribed about circle O and the sides of  ABC are tangent to the circle.  If AB = 20, AE = 12, and CF = 15, what is the length of AC?

Accepted Answer

27

Answer

15

Answer

8

Answer

23

Question 14

In the diagram below of circle O, diameter AB is perpendicular to chord CD at E.  If AO = 10 and BE = 4, find the length of CE.

Accepted Answer

8

Question 15

In the diagram, diameter DE is perpendicular to chord ST at point L.  Which statement is NOT always true?

Accepted Answer

RL = LE

Answer

(DL) (EL) = (SL) (TL)

Answer

SR = DR

Answer

SL = TL

Question 16

Secants PAC and PBD are drawn.  If PA = 9, PB = 10, and BD = 17, determine the length of AC

Accepted Answer

21

Question 17

In the diagram, diameter AB is perpendicular to chord CD at E.  If AE = 2 and FB = 17, then the length of CE is

Accepted Answer

8

Answer

7

Answer

16

Answer

15

Question 18

In the diagram, secants PQR and PST are drawn to a circle from point P.  If PR = 24, PQ = 6, and PS = 8, determine and state the length of PT.

Accepted Answer

18

Question 19

Use the diagram to determine the length of CD.

Accepted Answer

12

Question 20

In the diagram, if AE = 4, AB = 12, and DB = 6, what is the length of OC?

Accepted Answer

7

Answer

9

Answer

4.5

Answer

14

Question 21

Using the diagram, the length of BC is

Accepted Answer

12

Answer

20

Answer

16

Answer

15

Question 22

In the diagram, AC $\perp$ DB.  If DB = 34, AC = 30, and DE > BE, what is the length of BE?

Accepted Answer

9

Answer

25

Answer

16

Answer

8

Question 23

Secants JKL and JMN are drawn to circle O from an external point, J.  If JK = 8, LK = 4, and JM = 6, what is the length of JN?

Accepted Answer

16

Answer

8

Answer

10

Answer

12

Question 24

As shown in the diagram, tangents BA and BC are drawn.  If OA = 7 and DB = 18, determine and state the length of AB.

Accepted Answer

24

Question 25

In circle O, secants ADB and AEC are drawn from external point A. If AD = 8, AE = 6, and EC is 12 more than BD, the length of BD is

Accepted Answer

22

Answer

6

Answer

36

Answer

48

Question 26

In the diagram, chord DF bisects chord BC at E.  If BC = 12 and FE is 5 more than DE, then FE is

Accepted Answer

9

Answer

4

Answer

6

Answer

13

Question 27

In the diagram, tangent PA and secant PBC are drawn .  If PB = 3 and BC = 15, what is the length of PA?

Accepted Answer

3$\sqrt{6}$

Answer

3

Answer

3$\sqrt{5}$

Answer

9

Question 28

In the diagram RST and RQP are tangents.  If RS = 6, ST = 4, and RP = 15, what is the length of RQ?

Accepted Answer

4

Question 29

In the figure, quadrilateral TAEO is circumscribed around circle D. The midpoint of TA is R, and HO $\cong$PE .  If AP = 10 and EO = 12, what is the perimeter of quadrilateral TAEO?

Accepted Answer

64

Answer

76

Answer

56

Answer

72

Question 30

In the diagram below of circle O, chords JT and ER intersect at M.  If EM = 8 and RM = 15, the lengths of JM and TM could be

Accepted Answer

16 and 7.5

Answer

18 and 6.5

Answer

12 and 9.5

Answer

14 and 8.5

Question 31

In the diagram, tangent AD and secant ABC are drawn.  If CA = 12.5 and CB = 4.5, determine and state the length of DA.

Accepted Answer

10

Question 32