Explore Geometry Problem 778 - Unveiling the Intriguing Relationship between Side, Orthocenter Distance, and Circumradius in a Triangle. Perfect for High School and College Mathematics Education!

In a triangle, prove that the sum of the squares of one side and the distance from the orthocenter to the opposite vertex is four times the square of the radius of the circumcircle.

Geometry's realm speaks,
Triangle's secret unfolds:
Side and orthocenter,
Their sum and squared distance,
Fourfold the circumradius.