Families of Four-Point Touching Isosceles Triangles

This Demonstration shows four-point touching families of of isosceles triangles. The task is to find parameters so that the triangles form a four-point touching family.

Parameter is one-half of the smaller diagonal of the rhombus and is the altitude of the triangle.

A family is said to be -touching provided each element of has a nonempty intersection with precisely other elements of . A -touching family is said to be point--touching if any two touching sets have only a single common point [1].