Multiple Choice Practice Circles Geometry Level Geometry Index | Regents Exam Prep Center

 Also available in Hardcopy (.pdf): Circles

Directions:  Choose the best answer.  Answer ALL questions (or only a few at a time), then use the BUTTON at the BOTTOM of the page to check your answers.  If you are told that an answer is incorrect, go back and redo that question and CHECK ANSWERS again.   You may CHECK ANSWERS at any time.
You may use your graphing calculator when working on these problems.

1.  In the diagram at the right, the segments shown are tangent to the circle.  Find the value of x.
[1]  5
[2]  6
[3]  7
[4]  9

2.

[1]  50                [2]  60
[3]  80                [4]  100

3.  Given the circle at the right with two intersecting chords.
Find the length represented as x.
[1]  2                 [2]  6
[3]  8                 [4]  10

4.  In the accompanying diagram, tangent and secant
are drawn to circle O from point A, AB = 6 and
AC = 4.  Find AD.
[1]  5
[2]  9
[3]  10
[4]  13

5.  In the accompanying diagram of circle O, m<ABC = 2x and   Find the value of x.
[1]  20
[2]  40
[3]  60
[4]  80

 6.  In the diagram at the right, secant intersects circle O at D, secant intersects circle O at E,  AE = 4,  AC = 24,  and AB = 16.  Find AD.      [1]  4      [2]  5      [3]  6      [4]  10

7.  Given the circle at the right with diameter , find x.
[1]  30°
[2]  45°
[3]  60°
[4]  90°

8.  Given a circle with the center indicated.  Find x.
[1]  100
[2]  80
[3]  50
[4]  40

9.  Two chords intersect within a circle to form an angle whose measure is 53°.  If the intercepted arcs are represented by 3x + 3 and 10x - 14, find the measure of larger of these two arcs.
[1]  9                    [2]  13
[3]  30                  [4]  76

10. A cathedral window is built in the shape of a semicircle.  If the window is to contain three stained glass sections of equal size, what is the area of each stained glass section?  Express answer to the nearest square foot.
[1]  1 sq. ft.
[2]  3 sq. ft.
[3]  13 sq. ft.         [4]  26 sq. ft.

11.  Given the two secants shown in the diagram at the right, find the number of degrees in the angle labeled x.
[1]  40°
[2]  60°
[3]  80°
[4]  140°

12.  The number of common tangents that can be drawn for two externally tangent circles is

[1]  1                  [2]  2                  [3]  3               [4]  4

13.  Given tangent to the circle shown at the right.  Find the size of the arc designated by x.
[1]  25
[2]  50
[3]  100
[4]  260

14.  Given a circle with two secants as shown at the right.  Find the value of the arc designated by x
[1]
105
[2]  80
[3]  45
[4]  25

15.  Given the circle at the right with the indicated center.  Find the measure of the angle designated by x.
[1]  35
[2]  55
[3]  70
[4]  72.5

16.  Given the circle at the right with two tangents to the circle from a common external point.  Find the measure of the angle designated by x.
[1] 60

[2] 80
[3] 85
[4] 130

17.  in circle O at the right.
Which method for proving congruent triangles can be used to prove that ?
[1]  Side-Side-Side (SSS)
[2]  Side-Angle-Side (SAS)
[3]  Angle-Side-Angle (ASA)
[4]  All of the above.

18.  In the same circle, or congruent circles, congruent central angles have congruent arcs.
[1]  TRUE               [2]  FALSE

19.  Given the circle at the right with designated center, designated perpendicular, and radius 5.  Find the length of the segment labeled x.
[1]    4                     [2]    5
[3]    8                     [4]

20.
in circle O shown at the right.  Which two sets of congruent angles can be used to prove ?

[1]
[2]

[3]

[4]