Infographic Geometry Problem 1064: Triangle,
Orthocenter, Altitudes, Circumradius, Sum of the Squares
of Sides. Level: High School, SAT Prep, College, Mathematics Education

The figure shows a triangle ABC with
the orthocenter H and the circumradius R. If a, b, and c are the sides,
and AH =a_{1}, BH = b_{1}, and CH = c_{1}, prove
that a^{2} + b^{2} + c^{2} + a_{1}^{2} +
b_{1}^{2} + c_{1}^{2} = 12R^{2}.