Van Aubel’s Theorem for Triangles
Van Aubel’s Theorem describes a relationship between squares constructed on the sides of a quadrilateral.
In Martin Gardner's “Mathematical Circus,” pg 179, he shows generalizations of this theorem. This one is for triangles.
Starting with a triangle, construct a square on each side. In this case Van Aubel’s Theorem says that the line segment between
the centers of two of the squares and the line segment between a vertex of the triangle and the center of its opposite square
are of equal lengths and are at right angles to one another.
Draggable points are colored red.