The figure shows a triangle ABC. MD is the
perpendicular bisector of AC (D on BC) and NE is the
perpendicular bisector of BC (E on CA). MD and NE meet at O.
Prove that (1) CO and DE are perpendicular; (2) Points E, A, O,
D, and B are concyclic.
"There is geometry in the humming of the strings. There is music in the spacing of the spheres."
Pythagoras. ca.560-ca.480 BC.