
Intersecting Ellipse Triplet relates to Triangle incentre?
Posted:
Feb 6, 2010 12:36 PM


An ellipse having its foci at B and A and interfocal distance BA = c is drawn through vertex C of triangle CBA. The sides are a, c and b respectively. The ellipse has major axis (a+b) and semi minor axis sqrt(s(sc)), s = (a+b+c)/2. Likewise, other two ellipses drawn through A and B have interfocal distances a and b respectively.
I am attempting to guess how this triangle?s incentre I could be an interesting centre of this ellipse triplet combination. As CI is along normal for moving point C on the ellipse with moving BC/AB incident/reflected rays...
Posting it here FWIW, hoping it could engage your attention for a fuller result, may be using Java SketchPad.
Best Regards, Narasimham

