Show that $MNPQ$ is a square Let $ ABCD $ a quadrilateral s.t. $AC=BD $ and $m (\angle AOD)=30°$ where $O=AC\cap BD $.
Let $\triangle ABM, \triangle DCN, \triangle ADN, \triangle CBQ $ equilateral triangles with $Int (\triangle ABM)\cap Int (ABCD)=\emptyset$,  $Int (\triangle DCP)\cap Int (ABCD)=\emptyset$,  $Int (\triangle ADN)\cap Int (ABCD) \neq \emptyset$,  $Int (\triangle CBQ)\cap Int (ABCD)\neq\emptyset$.
Show that $MNPQ$ is a square.
I have no idea how to start.

I believe this is the desired result. Note that the intersection/non-intersection is opposite from the description.

