Automatic Proving Facilities of Cinderella

Activity Problem

In the opposite figure, What can you say about the three points F, C, and E in terms of collinearity? i.e. Are they collinear?










Conjecture

The three points F, C, and E are collinnear.
Please enable Java for an interactive construction (with Cinderella).

Hint

To automatically check the collinearity of the three points using Cinderella, open cdy file of the problem, then select Information Window from View menu, or Press Ctrl+5 to open Cinderella information window. Then, switch to the " Line, by two points" by press "Draw Connecting Line" tool to construct the line that connects the two points F and E for doing so move the mouse pointer toward the point F press the left mouse button, hold it then drag the mouse over point E then release the mouse button. Note the message that is given in the Cinderella Console Window, which indicates an automatic report about the collinearity of the three points.