Sphere + Plane = ?

In the applet below, notice that a plane intersects (slices through) a sphere. You can alter the position of the white plane by moving any 1 (or more) of the LARGE POINTS this plane passes through. You can control the size of the sphere by using the radius slider. Directions: 1) Slide the Slide Me! slider and carefully observe what happens. 2) After doing so, readjust the positions of the 3 blue points to create differently-positioned intersection. The slide the Slide Me! slider all the way back. Repeat step (2) a few more times. Then answer the question that appears beneath the applet. To explore this resource in Augmented Reality, see the directions below this applet.


How would you describe the cross section (intersection) of a plane and a sphere? Explain how what you observed helps support your assertion.


1) Open up GeoGebra 3D app on your device. 2) Go to the MENU (horizontal bars) in the upper left corner. Select OPEN. In the Search GeoGebra Resources input box, type wmahnyed (Note this is the resource ID = last 8 digits of the URL for this resource.) 3) In the resource that uploads, zoom in/out if needed. While viewing in Augmented Reality:  Move sliders a_1, b_1, c_1 to control the location of one purple point. Move sliders a_2, b_2, c_2 to control the location of the orange point. Move sliders a_3, b_3, c_3 to control the location of the blue point. And of course, slide the SlideMe slider to animate.