Let three similar Isosceles Triangles ,
, and be constructed on the sides of a Triangle
. Then the Envelope of the axis of the Triangles
and is Kiepert's parabola, given by
|
(1) |
|
(2) |
where are the Trilinear Coordinates for a line tangent to the parabola. It is tangent to the sides of
the Triangle, the line at infinity, and the Lemoine Line. The Focus has Triangle Center
Function
|
(3) |
The Euler Line of a triangle is the Directrix of Kiepert's parabola. In fact, the
Directrices of all parabolas inscribed in a Triangle pass through the
Orthocenter. The Brianchon Point for Kiepert's parabola is the
Steiner Point.
See also Brianchon Point, Envelope, Euler Line, Isosceles Triangle,
Lemoine Line, Steiner Points
© 1996-9 Eric W. Weisstein
1999-05-26