Class discussion / debrief

Think, Pair, Share

  1. How do you find the circumference of a circle given the radius? Given the diameter?
  1. In a circle, how do you find the length of an arc given its central angle?
  1. In a circle, what is the relationship between arcs and chords?
  1. In a circle, what is the relationship between an inscribed angle and its intercepted arc?

Watch Out!

  • Difference between radius and chord
  • Find the correct arcs

Vertex of inscribed angle is on the circle
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

Station 1

  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. RadiusDiameter

Relationship?

4. What is  ?

5. What is  times twice your radius?

Does this match your answer to #1? Why or why not?

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:
Central AngleAOB

O is the center of the circle

Inscribed AngleCOD

O is on the circle


Chord

Tangent

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?

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?
  1. Copy the horizontal and vertical radii.

What fraction of the circle’s circumference is this arc?

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?

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?

4. Mark the center C. Copy the radii.

Find the measure of arc AB.

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.

  1. Mark points P, A and B. Draw the chords.

What is the measure of the inscribed angle?

  1. Label the center point C. Draw the two radii.

Find the measure of arc AB.

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:

  1. Circle with radius 5 cm and central angle 30
  1. Circle with diameter 7 inches and central angle 145
  1. Circle with radius 0.5 meters and central angle 270
  1. Circle with diameter 14 feet and central angle 315

Station 3

Copy the 3 inch diameter circle with center P.

  1. What is the circumference?
  1. Copy the 2 radii, mark the 40 angle, copy the chord.

What is the length of the chord AB?

What is the length of the arc AB?

  1. 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?

Station 3 continued

  1. Describe the relationship between chords and arcs your group discovered.
  1. What is the relationship between PAB and PCD? Explain
  1. What is the relationship between the measures of arc AB and arc CD? Explain.
  1. 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?