Areas of Squares from the Pedals of a Triangle
For a triangle and a point , let , and be the projections of the point to the opposite sides. Then is called the pedal triangle of .[more]
Construct squares on the segments , , , , and and color them alternately blue and green. Bottema's theorem states that the sum of the areas of the three squares of one color equals the sum of the squares of the other color.
Drag to vary the shape of .[less]
 Z. Cerin, "Rings of Squares Around Orthologic Triangles," Forum Geometricorum, 9, 2009 pp. 57–80. forumgeom.fau.edu/FG2009volume9/FG200906.pdf.