Right is right

Geometry Level pending

Two right isosceles triangles are inscribed in a quadrilateral. Their right angles are at opposing vertices of the quadrilateral. Their other vertices are midpoint of its sides. Find the largest angle of the quadrilateral.

Details:\( AF=FB,BG=GC,CH=HD,DE=EA\)

\(\angle ECF=90^\circ, \angle HAG=90^\circ, AH=AG, CE=CF\)

Drawing is not to scale.

Inspiration: Just one step to regularity of quadrilateral by Rohit Camfar.


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