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

Problem

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problem

Find all quadrilaterals ABCDABCD such that all four triangles DABDAB, CDACDA, BCDBCD and ABCABC are similar to one-another.
Plain-text mathematical notation (without MathML)
Find all quadrilaterals ABCD such that all four triangles DAB, CDA, BCD and ABC are similar to one-another.
Original LaTeX notation
Find all quadrilaterals $ABCD$ such that all four triangles $DAB$, $CDA$, $BCD$ and $ABC$ are similar to one-another.

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