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 L_{a}(t), L_{b}(t) and L_{c}(t)

3.2,3

Locus of perspector
of triangle bounded by L_{a} (t), L_{b} (t), Lc
(t) 
3.4

Orthology of
ABC and the triangle bounded by L_{a} (s),
L_{b} (s), Lc (s) 
4

The triangle
bounded by L'_{a}(t), L'_{b}(t), L'_{c}(t)

5

The lines L_{a}(a),
L_{b}(b), L_{c}(c)

6 
The lines L_{a}(a),
L_{b}(b), L_{c}(c) and related triangles

7 
The lines L_{a}(sa), L_{b}(sb), L_{c}(sc)
and the extouch triangle 