Sphere Cross Sections Investigation

In the GeoGebra file below, use the tools to investigate the cross sections formed by slicing a plane through the three points located on the surface of a sphere.

Investigation Directions:

Attempt to answer the questions below before playing with the file here.Then move the points A, B, and C around on the surface of the sphere.

1. What is the shape of the cross section formed by slicing the sphere above with the single plane through all three points A, B, and C? (Use the initial positions of points A, B, and C if you moved the points reset the GeoGebra file)

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2. What cross section shapes can be formed by moving points A, B, and C anywhere along the surface of the sphere, being sure the 3 points are not collinear?

3. Which of the following statements is TRUE about the cross sections of a sphere?

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4. Can you position the points so that the cross section created is an ellipse, parabola, and/or a polygon? (add a comment and explain why, or why not?)

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