Honors Math 2
Name:
Date:
Chapter 8 Review Problems
1. Circle Q and Circle R are congruent circles that intersect at C and D. CD is called the
common chord of the circles.
C
a. What kind of quadrilateral is QDRC? Why?
b. CD must be the perpendicular bisector of QR . Why?
c. If QC = 17 and QR = 30, find CD.
Q
R
D
2. Quadrilateral ABCD is circumscribed about a circle. Discover
and prove a relationship between AB + DC and AD + BC.
(see homework p690 #1)
3. JK is tangent to circle P and circle Q.
a. Find the length of JK
(Hint: draw a segment from Q perpendicular to JP)
b. What kind of quadrilateral is JPQK?
J
K
P
4. Given:
Prove:
11
3
3
Q
Circle O and Circle Q intersect at R and S
measure of arc RVS = 60 and
measure of arc RUS = 120
OR is tangent to circle Q
QR is tangent to circle O
5. Circle O has radius 10 and chord XY is 8 cm long. How far is the chord from the O?
6. Quadrilateral ABCD is inscribed in a circle.
mD  75,arc AB  x 2,arc BC  5x, and arc CD  6x . Find x and m A

7. Equilateral triangle ABC is inscribed in a circle. P and Q are midpoints of arc BC and arc
CA respectively. What kind of figure is quadrilateral AQPB? Justify your answer.
8. A quadrilateral circumscribed about a circle has angles of 80,90,94,96. Find the
measures of their four non-overlapping arcs determined by the points of tangency.
9. The diagram shows two circles that share the same center. Write an
equation involving arcs a, b, and c.
b
c
a
C
B
10. AC and AE are secants of circle O. It is given that AB  OB .
Discover and prove a relation between the measures of
arcs CE and BD.
A
O
D

11. A Ferris wheel has diameter 42 feet. How far will a rider travel during a 4 minute ride if the
wheel rotates once every 20 seconds?
12. Find the radius (the distance from the center to a vertex in a regular polygon) and the area of
the regular hexagon whose perimeter is 12 3 and apothem is 3 .
I
13. Find the area of the region bounded by arc IK and chord IK.
60°
J
K
3
14. A rectangle with length 16 cm and width 12 cm is inscribed in a circle. Find the area of the
region inside the circle but outside the rectangle.
15. Here XY has been divided into five congruent segments and semicircles have been drawn.
But suppose XY were divided into millions of congruent segments and semicircles were
drawn. What would the sum of the lengths of the arcs be?
X
Y
16. If mAOB  108 and radius of circle O is 5 2 , find the length of arc AB and the area of
sector AOB.
E
P
17. The diagram shows an angle QRP that makes a
linear pair with an inscribed angle.
Identify an arc of the circle whose degree measure
is 2 · QRP.
Write a proof supporting your answer.
Q
O
R
S
Answers
1a. rhombus since the circles are congruent, all the radii are congruent.
b. The diagonals of a rhombus are perpendicular bisectors of each other.
c. 16
2. AB + DC = AD + BC
3a. 15
b. trapezoid
4. Hint for proof: show ORQ  OSQ
5. 2 21 cm
6. x = 10, m A =55°
7. rectangle 
   
8. 100
,90 ,86 ,84
9. b – a = c
10. arc CE is 3 times arc BD
11. 504  1583 feet
12. radius = 2 3 , area = 18 3

13.
6  9 3
4
14. 100
 192cm2
15. the sum of the arc lengths is

( XY ) no matter how many segments are used.
2
Proof: Let n = number of segments;
 XY 
length of each arc = r   
;
 2n 
 XY  
sum of arc lengths = n 
   XY 
 2n  2
16. Arc length = 3 2
Area of sector = 15
17. Answer: arc PRS.
Proof: QRP + PRS = 180°.
2QRP + 2PRS = 360°.
2QRP = 360° – 2PRS.
But PRS is an inscribed angle, so by the Inscribed Angle Theorem, 2PRS = m arc PS.
Also, m arc PS + m arc PRS = 360° because arcs PS and PRS together make the whole circle.
So, m arc PRS = 360° – m arc PS = 360° – 2PRS = 2QRP.