IGO 2019 I2

Find all quadrilaterals $ABCD$ such that all four triangles $DAB$ , $CDA$ , $BCD$ and $ABC$ are similar to one-another.

Proposed by Morteza Saghafian

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.