REVIEW 6
Circles and Conics
These review questions bring together the ideas from Chapters 12 and 13. This is your chance to test your knowledge of circles and related conics. Answer all the questions, and try to express your thinking as clearly as you can.
Use the figure below for questions 1 through 3.
1. Name a chord.
2. Name an inscribed angle.
3. How is the angle is question 2 measured?
4. If the circumference of circle O is 24π, what is the radius of circle O?
5. The two circles in the figure below are concentric. The diameter of the smaller circle is half the diameter of the larger circle. What fraction of the large circle is shaded?
6. In the figure below, circle C is internally tangent to circle O and O is a point on circle C. m∠OAE = 30°. If 
is π cm long, how long is 
?
7. Tangents 
and 
are drawn to circle O from point P outside the circle, forming ∠RPQ, which measures 20°. Chord 
is drawn. Find the measure of ∠PQR.
8. Chord 
and chord 
intersect at point E inside circle O. If AE = x, EB = 3x, CE = 2x, and ED = x + 2, find the length of .
9. In the circle described in question 8, if 
= 72° and 
= 64°, find m∠AEC
10. Radii 
and 
are drawn in circle O, and point C lies on circle O. 
is a major arc. Acute angle ∠AOB is a central angle that measure 48°. Find the measure of ∠ACB.
11. Secants 
and 
are drawn to circle O from point P outside the circle, as shown in the figure below. PB = 3 cm, PC = 5 cm, and AB = 17 cm. Find the length of 
.
12. Construct tangents to circle O from point P using compass and straightedge.
13. If regular hexagon ABCDEF is inscribed in circle O, find the measure of 
.
14. From a point P outside circle O described in question 13, two tangents are drawn, one to B and one to F. Find the measure of ∠BPF.
15. In a certain circle C, an angle of 85°, formed by radii 
and 
, defines a sector with an area of 34 square inches. What is the length of arc 
?
16. What is the radian equivalent of 120°?
17. What is the equivalent degree measure for an angle of 
radians?
18. Sketch a graph of 
.
19. Write the equation of the circle shown below.
20. Identify each equation below as circle, ellipse, parabola, or hyperbola.
a) 
b) 
c) 
d) 