Example

Click the Open Problem button and select the file beetle.xml in the vanilla folder.

Here's the problem:

A beetle crawls on the surface of this pyramid from some point on edge AC up to the top so covering a distance double to the height of the pyramid. Reconstruct the beetle's path.

Click the Create Solution button to start solving the problem.

In Geometria, measurements and drawings can only be done on the surface of the figures. However, the height of the pyramid is contained in its interior. To be able to measure the height, we will have to cut the pyramid with a plane through D perpendicular to the pyramid's base. We will do that in 3 steps.

First, draw a pependicular through D to BC. Click the Draw Perpendicular button and fill in the labels.

Second, draw a perpendicular through E to BC. The easiest way to do that, by the way, is to select point E and segment BC (hold down the Ctrl key as you do that), popup a menu and select Draw Perpendicular from that menu. Choose the face in which to draw the perpendicular.

Third, cut the pyramid through points D, E, F. Again, to save time, select segments DE and EF, popup a menu and select Cut Figure from that menu.

Select one of the two fragments of the pyramid, say Figure 1, and draw a perpendicular through its apex to its base. This would be the height of the pyramid.

Measure the height and assign a variable to the result. The variable will be copied to the notepad.

Now, select again the pyramid, double the the variable Height and lay that distance off D to AC. Again, to save time, have the variable selected on the notepad, as well as point D and segment AC in figure Pyramid.

Select Answer from the Edit menu and enter G, D, separated by a comma. Again, no input will be necessary if you have points G, D selected ahead of time.