Van Schooten's theorem
Van Schooten's theorem, named after the Dutch mathematician Frans van Schooten, describes a property of equilateral triangles. It states:
The theorem is a consequence of Ptolemy's theorem for concyclic quadrilaterals. Let be the side length of the equilateral triangle and the longest line segment. The triangle's vertices together with form a concyclic quadrilateral and hence Ptolemy's theorem yields:
Dividing the last equation by delivers Van Schooten's theorem.
