When you hit the display relationship box, what is the relationship of the products as you move the points around the circle?
Now let's think about why that is the case.
What is the relationship of [math]\angle EGD[/math] and [math]\angle CGF[/math]?
Next, move point E so that it is overlapping with point C. What do you notice about [math]\angle E[/math] and [math]\angle C[/math]?
Now look at the two triangles that are formed. [math]\bigtriangleup EGD[/math] and [math]\bigtriangleup CGF[/math]. With the information in the two previous questions, what do you know about relationship of these two triangles?