IR-MO 2003 Problem 18

In tetrahedron $ABCD$ , radius four circumcircles of four faces are equal. Prove that $AB=CD$ , $AC=BD$ and $AD=BC$ .

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.