Sphere with Center Through Point [icon]/images/ggb/toolbar/mode_sphere2.png[/icon][br]Sphere with Center and Radius [icon]/images/ggb/toolbar/mode_spherepointradius.png[/icon][br]Midpoint or Center [icon]/images/ggb/toolbar/mode_midpoint.png[/icon][br]Point on Object [icon]/images/ggb/toolbar/mode_pointonobject.png[/icon][br]Segment [icon]/images/ggb/toolbar/mode_segment.png[/icon][br][color=#1e84cc][br][b]In this exercise, we'll learn how to use these tools to explore the cross section of any two spheres that intersect in more than one point. [/b][/color]

1) Use the SPHERE WITH CENTER THROUGH POINT [icon]/images/ggb/toolbar/mode_sphere2.png[/icon] tool to create a sphere. [br] Then select the MOVE [icon]/images/ggb/toolbar/mode_move.png[/icon] arrow to deselect this sphere tool (i.e. turn this tool off). [br] You should be able to drag point [i]A[/i] (center of sphere) and [i]B[/i] (which determines the sphere's radius). [br][br]2) Use the SPHERE with CENTER and RADIUS [icon]/images/ggb/toolbar/mode_spherepointradius.png[/icon] tool to create a sphere with radius = 4. [br] After doing so, select the MOVE [icon]https://www.geogebra.org/images/ggb/toolbar/mode_move.png[/icon] arrow to deselect this sphere tool. [br][br]3) Move any one or both of these spheres around so that they intersect (overlap) each other. [br] After doing so, right click on the gray plane. Uncheck "Show Plane" to hide this gray plane. [br][br]4) Use the INTERSECT 2 SURFACES [icon]https://www.geogebra.org/images/ggb/toolbar/mode_intersectioncurve.png[/icon] tool. Select one sphere. Then select the other sphere. [br] You should notice GeoGebra now plots the intersection of both of these 2 surfaces. [br][br][b][i]Keep going: More directions appear below the applet. [/i][/b]

5) Select the MOVE tool to deselect this tool you've just used in step (4). Move the spheres around now. [br] Just be sure they still intersect each other. What does this intersection look like? [br][br]6) Now select the MIDPOINT OR CENTER [icon]/images/ggb/toolbar/mode_midpoint.png[/icon] tool. Select ONLY the intersection of these 2 surfaces[br] (that you created in step 4). [br][br]7) Select the POINT ON OBJECT [icon]/images/ggb/toolbar/mode_pointonobject.png[/icon] tool. Then select the intersection of both spheres (that you plotted [br] in step (4)). Repeat this process again to put a second point on this intersection. [br][br]8) Use the SEGMENT [icon]/images/ggb/toolbar/mode_segment.png[/icon] tool to construct the segment connecting the point you created in steps (6) [br] and any one of the 2 points you created in step (7). Then select the MOVE tool. Click on the segment [br] to show the style bar. Click on the [b]A[/b] icon. Deselect "Name" and select "value". Now move the endpoint[br] of the segment on the intersection around. What do you notice?

[color=#0000ff]When you're done (or if you're unsure of something), feel free to check by watching the quick silent screencast below the applet.[/color]