# The Brocard Disc

Please enable Java for an interactive construction.

The above applet calculates the positions of various centres of a reference triangle ABC, and additionally plots these relative to the disc of diameter OSym (the disc enclosed by the Brocard circle). It is offered to lend weight to the hypotheses advanced (generally without mathematical proof) in section 4 of my report "Applications of the GPAT to triangle geometry", which you can find more about here.

The points are as follows:

 Icon Object Label Black point Circumcentre O Dark red point Symmedian point Sym Red point Centroid G Blue point Gergonne point Ge Green point Incenter I Orange point Mittenpunkt M Grey points Isodynamic points S and S' Grey Circle Circle of diameter OSym (Brocard circle) DOSym Red Circle Circle of diameter OG DOG Purple Circle Parry circle P

The triangle vertices, points A,B and C, can be moved and the other points will be re-calculated as a result; the disc can be repositioned for convenience- the circumcentre can be moved freely whilst the Symmedian point is naturally constrained to the circle boundary.

Applet development in Cinderella