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Math Forum » Discussions » Math Topics » geometry.puzzles.independent

Topic: Intersecting Ellipse Triplet relates to Triangle in-centre?
Replies: 7   Last Post: Apr 18, 2010 2:59 PM

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narasimham

Posts: 2,537
Registered: 12/6/04
Intersecting Ellipse Triplet relates to Triangle in-centre?
Posted: Feb 6, 2010 12:36 PM
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An ellipse having its foci at B and A and inter-focal 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(s-c)), s = (a+b+c)/2. Likewise, other two ellipses drawn
through A and B have inter-focal distances a and b respectively.

I am attempting to guess how this triangle?s in-centre 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

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