a. Although the extra pictures, with angles inscribed at G and H, show in one static picture the invariance of an angle subtending chord EA, it is probably better, in proving this result, to delete those extra points and segments: G, H, GE, GA, HE, and HA. Diagram 3' shows the streamlined diagram. You can drag D to see the different possibilities.

b. Construct both the diameter through point D and the segment OE.

c. By using the result of #2 above and looking at angles as sums or differences of other angles, (e.g., angles ODE and AD) prove that any angle inscribed in the circle subtending chord EA is half the central angle subtending EA.

Diagram 3

Diagram 3'