RO-NMO 2003 Problem 111

Find the locus of the points $M$ that are situated on the plane where a rhombus $ABCD$ lies, and satisfy: $MA\cdot MC+MB\cdot MD=AB^2$ Ovidiu Pop

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.