Investigations with Circles

Objective: Have the students discover some properties of circles using GSP.

<>Lesson:  The following three activities are sort activities that can all be completed in one class period: They can be given as a packet or to each individual student as he completes each assignment.

1) Have the students investigate the property that any line tangent to a circle is in fact perpendicular to the radius of the circle and any two tangent lines are equal in length. For the Activity click here. For the GSP sketch showing the first property click here. For a GSP sketch showing the second property click here.

2) Have the students discover the formula for the measure of an arc of a circle. For the Activity click here. For the GSP sketch showing this property click here.

3) Have the students investigate the property that the measure of the central angle is twice the measure of the inscribed angle with the same endpoints. For the Activity click here. For the GSP sketch showing this property click here.

Conclusion:  Discuss the various properties of circles with the students and what conclusions they came to from working through their activities.

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Next:  Day 3
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Developed by Katherine Huffman