Orientation in an Napoleon-like situation

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Take a convex quadrilateral ABCD.

Define M such that AMB is a right triangle and AM=BM and is in the half-plane delimited by (AB) and not containing C.

Similarly, one can define BNC, CPD et DQA.

It seems natural that the triangles AMB, BNC, CPD and DOA have the same orientation. But how can we prove this fact?