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:


Black pointCircumcentreO
Dark red pointSymmedian pointSym
Red pointCentroidG
Blue pointGergonne pointGe
Green pointIncenterI
Orange pointMittenpunktM
Grey pointsIsodynamic pointsS and S'

Grey CircleCircle of diameter OSym (Brocard circle)DOSym
Red CircleCircle of diameter OGDOG
Purple CircleParry circleP

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