Archimedes' Midpoint Theorem

Archimedes' Midpoint Theorem:

M is the midpoint of arc AMB. Choosing any point C on the arc MB (as shown), we draw MD perpendicular to AC. Then AD = DC + BC.

Here you can move the points A, B, and C:

Please enable Java for an interactive construction (with Cinderella).

The above Java interactive demonstration was created with Cinderella (a geometry program).