To do this part of the lesson, download this Geometer's Sketchpad file.

You will also need to use either of the 5 bolt pattern files.

Use the 5 bolt GSP file to answer the following.

STEP 1: Measure the circumference of the circle.

STEP 2: Now measure all 5 chord lengths. BC, CD, DE, EF, FB

STEP 3: Add the 5 chord lengths together.

STEP 4: How close are your answers to STEP 2 and 3.

STEP 5: Now find the Bolt Circle Diameter for the 5 bolt pattern.

Use the 20 bolt GSP file to answer the following.

STEP 1: Measure the circumference of the circle.

STEP 2: Now measure the chord length BC

STEP 3: Multiply your answer to STEP 2 by 20 to find the sum of all the chord lengths together.

STEP 4: How close are your answers to STEP 2 and 3.

STEP 5: Compare your answers for the 5 bolt and 20 bolt problems. In other words, which answer is closer to the circumference you measured, the 5 bolt or the 20 bolt tire?

STEP 6: Can you make a conclusion about the circumference of a circle and the sum of the chord lengths as the number of lug nuts increases?

STEP 7: Now find the Bolt Circle Diameter for the 20 bolt pattern.

STEP 8: Divide your answer to STEP 1 by your answer to STEP 7. Does this number look familiar? Explain.

To find the circumference of a circle, the formula is C = (Pi)D, where D is the diameter of the circle (or in this case, the BOLT CIRCLE DIAMETER) and Pi is the special number you found in STEP 8.