Details

This Demonstration is based on [1, pp. 128, 129]. The proof from [1] follows.

Let the line parallel to that passes through intersect at . So . Then, since bisects , . Also, since , we have . With , by two applications of the Pythagorean theorem,

,

which reduces to the quartic equation

.

Fortunately, this quartic easily factors as . Since , .

Reference

[1] G. E. Martin, Geometric Constructions, New York: Springer, 1998.