ZA-SAMO 2002 Problem 1

Given a quadrilateral $ABCD$ such that $AB^2 + CD^2 = AD^2 + BC^2$ , prove that $AC \perp BD$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.