EMAT 6700

Review Problems: Circles

by Doug Westmoreland

Points A, B, and C lie on circle O.

1. Segment AC is called a __________, while line AC is called a ____________.

2. Segment OB is called a ___________.

3. The best name for segment AB is __________.

4. Triangle ABC is ____________ in circle O.

Lines ZX and ZY are tangent to circle P.

5. Segment PX, if drawn, would be _________ to line XZ.

6. If the radius of circle P is 6 and if XZ = 8, the distance between points P and Z is ___________.

7. If measure of angle Z is 90 and if XY = 13, the distance between points X and Y is _________.

8. If measure of angle 1 is 42, the measure of arc JK is _____________.

9. If measure of arc JN is 120 and measure of arc NL is 130, then measure of arc JOL is _________.

10. Suppose ray JO intersects circle O at point G.

a) measure of arc JLG is _____________.

b) If angle NOG is congruent to angle KOL, then arc NG _____ arc KL.

In circle X, the measure of arc AC is 120.

11. Measure of arc AB is _____________.

12. If segment AC is congruent to segment CD, then measure of arc CD is _________.

13. If CD > AC , then XF _____ XE. ( < , =, > )

14. If DC = 24 and XF = 5, the radius of circle X = _____________.

Line RS is tangent to the circle at point N.

15. If the measure of angle K is 105, then measure of angle PNL is ____________.

16. If the measure of arc PN is 100, then measure of angle PLN is _________ and the measure of angle PNR is ___________.

17. If the measure of angle K is 110, then the measure of arc PNL is ________ and measure of arc PL is __________.

18. If the measure of arc AC is 40 and the measure of arc BD is 60, then the measure of angle 1 is __________.

19. If the measure of arc AC is 44 and the measure of angle 1 is 55, then the measure of arc BD is ______________.

20. If the measure of arc EG is 100 and the measure of arc DF is 40, then the measure of angle EPG is ___________.

21. If segment PH is a tangent and the measure of arc GH is 90 and the measure of angle GPH is 25, then the measure of arc FH is _______________.

Chords, secants, and a tangent are shown. Find the value of x.

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