Class discussion / debrief
Think, Pair, Share
1. How do you find the circumference of a circle given the
radius? Given the diameter?
2. In a circle, how do you find the length of an arc given its
central angle?
3. In a circle, what is the relationship between arcs and
chords?
4. In a circle, what is the relationship between an inscribed
angle and its intercepted arc?
Name _______________________________ hr ___
Circle Stations
Station 1
Measure radius, diameter, circumference
Derive relationships among them
Station 2
Construct circle, radii, central angles, arc
Derive relationship arc and circumference
Find length of an arc
Station 3
Construct circle, radii, chords
Derive relationship chords, arcs, triangles
Solve real world problem
Station 4
Construct circles, inscribed angles, central angles
Find degree measures inscribed angels and its intercepted arc
Derive relationships among them
Watch Out!
 Difference between radius and chord
 Find the correct arcs
Vertex of inscribed angle is on the circle
Back Cover
Front Cover
Station 1
Central Angle AOB
O is the center of the circle
1. What is the mathematical name for the distance you found?
Measurements from other members of your group:
What is the distance around the edge of the lid in inches?
3. Radius
Diameter
Relationship?
4. What is  ?
5. What is  times twice your radius?
Does this match your answer to #1? Why or why not?
Inscribed Angle COD
O is on the circle
6. What is  times your diameter?
Does this match your answer to #1? Why or why not?
7. Do your answers #5 and #6 match? Why or why not?
8. Formula for circumference using radius:
Formula for circumference using diameter:
Chord
Station 1 continued
9. Larry installed a circular pool in his backyard. The pool has
a diameter of 20 feet. What is the circumference of the pool?
Tangent
10. Lisa is running for class president and passes out buttons
that each have a circumference of 6.28 inches.
What is the radius of each button?
Station 2
1. Copy the circle with a diameter 2 inches. Label the center
of the circle as point C. What is the circumference of the
circle?
Station 4 continued
3. Copy the second circle with radius 2 inches.
Mark points P, A and B.
Draw the chords and mark the inscribed angle.
What is the measure of the inscribed APB?
2. Copy the horizontal and vertical radii.
What fraction of the circle’s circumference is this arc?
4. Mark the center C. Copy the radii.
Find the measure of arc AB.
What is the ratio between the central angle and the total
angle measure of the circle? Justify.
3. How can you use the circumference of the circle and the
ratio of the central angle to find the total measure of the circle
to the length of the arc?
5. What relationship between the measure of an inscribed
angle and its intercepted arc did your group discover?
Station 4
Copy the circle with radius 0.75 inches.
Station 2 continued
4. In general, what method did your group discover to find the
length of an arc when you know the central angle?
Find the length of the arc:
5. Circle with radius 5 cm and central angle 30
1. Mark points P, A and B. Draw the chords.
What is the measure of the inscribed angle?
6. Circle with diameter 7 inches and central angle 145
2. Label the center point C. Draw the two radii.
Find the measure of arc AB.
7. Circle with radius 0.5 meters and central angle 270
8. Circle with diameter 14 feet and central angle 315
Station 3
Copy the 3 inch diameter circle with center P.
Station 3 continued
4. Describe the relationship between chords and arcs your
group discovered.
5. What is the relationship between PAB and PCD?
Explain
1. What is the circumference?
2. Copy the 2 radii, mark the 40 angle, copy the chord.
What is the length of the chord AB?
6. What is the relationship between the measures of arc AB
and arc CD? Explain.
What is the length of the arc AB?
3. Copy the next 2 radii, mark the 40, copy the chord
What is the length of chord CD?
What is the length of arc CD?
7. An apple pie 10 inches in diameter is cut into 6 equal
slices. What is the length of the chord for each slice of pie?