So AG=AE
Angle EAG=90 degrees
Because the quadrilateral ABCD is a square
So AB=AD
Angle error =90 degrees
Angle DAC=45 degrees
Because DAG= EAG+ DAE=90+ DAE.
BAE= BAD+ DAE=90+ DAE。
So angle DAG= angle BAE
So triangle DAG and triangle BAE are congruent (SAS)
So angle AGM= angle AEH
Because angle AGM+ angle EAG+ angle AMG= 180 degrees.
So angle AGM+ angle AMG=90 degrees.
Because angle AMG= angle HME
So AEH angle +HME angle =90 degrees.
Because angle HME+ angle AEM+ angle MHE= 180 degrees.
So MHE angle =90 degrees
So EB is perpendicular to GD.
(2) It is proved that the intersection D makes DN perpendicular to AC in n..
So angle DNA= angle DNG=90 degrees.
Because the angle DAC=45 degrees
Angle DAC+ angle ADN+ angle DNA= 180 degrees.
So the angle ADN=45 degrees
So angle ADN= angle DAC=45 degrees.
So DN=AN
In the right triangle DNG, the angle DNG=90 degrees.
So DG 2 = DN 2+NG 2.
Tangent angle AGH=DN/NG=3/4.
NG=AG+AN
AG= root number 2
So DG=5 times the root number 2.
Because triangle DAG and triangle BAE are congruent (proved)
So DG=EB
So EB=5 times the root number 2.