7.  This Sketchpad project will show the animated motion of a circle tangent to the sides...

7.  This Sketchpad project will show the animated motion of a circle tangent to the sides of an angle.

[1] Construct two rays  and  Locate point D on ray .

[2] Construct the bisectors of  ∠ADC and ∠ACD.

[3] Select, or construct, the intersection E of the two bisectors. Hide the bisectors.

[4] With E selected, select ray  and choose Perpendicular Line under CONSTRUCT.

[5] Select the point of intersection F of the perpendicular and ray , then Construct a circle with center E passing through F. (This circle should be tangent to both rays.) Hide the perpendicular.

[6] Select the circle and its center E to trace. (Use Trace under DISPLAY.) What happens when you drag point D?

[7] Select point D and ray  to animate the circle and its center. (Choose Animate under DISPLAY, and choose the options Bidirectionally and Quickly.)

What happened? What conjecture could be made? Try to prove it.