Inner/Outer Triangles

Author:
Terry Tam
Topic:
Triangles
For triangle ABC and an arbitrary point P, - Triangle DEF is the medial triangle (all vertices are midpoints of the original triangle sides) - Triangle GHI is the orthic triangle (all vertices are feet of attitudes of original triangle vertices to the opposite sidelines) - Triangle RST is the cevian triangle of point P (all vertices are the intersection points of the lines joining point P and the original triangle vertices to the opposite sidelines) - Triangle PAPBPC is the pedal triangle of point P (all vertices are the feet of attitudes of point P to the original triangle sidelines) Try to drag point P (even outside the triangle ABC) or triangle vertices (even crossing the opposite side) to see the changes of four triangles.