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 =a1, BH = b1, and CH = c1, prove
that a2 + b2 + c2 + a12 +
b12 + c12 = 12R2.