Dynamic Triangle Geometry:
Families of Lines with Equal Intercepts
Paul Yiu
Department of Mathematical Sciences
Florida Atlantic University

To appear in International Journal of Computer Learning of Mathematics.

[ps file][pdf]

Section
Sketches
1
The four classical triangle centers: centroid, circumcenter, incenter, orthocenter
1
More triangle centers: Gergonne point, Feuerbach point, Nagel point
2.1
The line L(t) cutting equal intercepts on AC and AB
2.2,3 Parabola tangent to the sidelines of a triangle
2.4,5,6
The envelope of L(t): inscribed parabola with focus the midpoint of arc BAC
2.7
The Simson lines of the midpoints of arc BAC, CBA, ACB concur at the incenter of the medial triangle
3.1
Triangle bounded by La(t), Lb(t) and Lc(t)
3.2,3
Locus of perspector  of  triangle bounded by  La (t), Lb (t), Lc (t)
3.4
Orthology of ABC and the triangle bounded by La (s), Lb (s), Lc (s)
4
The triangle bounded by L'a(t), L'b(t), L'c(t)
5
The lines La(a), Lb(b), Lc(c)
6 The lines La(-a), Lb(-b), Lc(-c) and related triangles
7 The lines La(s-a), Lb(s-b), Lc(s-c) and the extouch triangle