So angle B= angle D=90 degrees.
OCF angle =45 degrees.
AB=AD=BC=DC
Because AE=AF
So the right triangle ABE and the right triangle ADF are congruent (HL)
So BE=DF
(2) The quadrilateral AEMF is a diamond.
Proof: because BC=BE+CE (proved)
DC=DF+CF (certification)
BE=DF (certification)
So CE=CF
Because angle OCE= angle OCF=45 degrees (proved)
OC=OC
So triangle OCE and triangle OCF are congruent (SAS)
So OE=OF
Angle COE= angle COF
Because angle COE+ angle COF= 180 degrees.
So angle COE= angle COF=90 degrees.
So EF is perpendicular to AM.
Because OM=AM
So AM and EF are equally divided. AM and EF are perpendicular to each other.
So the quadrilateral AEMF is a diamond.