Conic by half-turn

Prove that if A', B', C' are the images of any three points A, B, C after a half-turn about O, then the six points A', B', C', A, B, and C lie on a conic.

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

Drag points A, B, C or O to change the conic.

View completed construction at Halfturn conic 2

Created by Michael de Villiers, 14 Nov 2007 with Cinderella