CD is perpendicular to AB and d

So angle BDC= angle ADC=90 degrees.

Because angle BDC+ angle ABC+ angle DCB= 180 degrees.

So the angle DCB=45 degrees

So angle ABC= angle DCB=45 degrees.

So DB=DC

Because angle DBF+ angle DFB+ angle BDC= 180 degrees.

So DFB angle +DBF angle =90 degrees.

Because BE is perpendicular to AC and e.

So GEC angle =90 degrees.

Because GEC angle +EFC angle +ECF angle = 180 degrees.

So EFC angle +ECF angle =90 degrees.

Because angel ·DFB = angel ·EFC

So angel ·DBF = angel ·ECF

So in triangle DBF and triangle DCA,

Because DB=DC (authentication)

Angle BDF= Angle ADC=90 degrees (confirmed)

Angle DBF= Angle ECF (confirmed)

So triangle DBF and triangle DCA are congruent (ASA)

So BF=AC

(2) Proof: Because Be bisects the angle ABC

So angle ABE= angle CBE

Because BE is perpendicular to AC

So AEB angle = CEB angle =90 degrees.

Because BE=BE

So the right triangle AEB and the right triangle CEB are congruent (ASA)

So AE=CE= 1/2AC.

Because BF=AC (authentication)

So CE= 1/2BF.

(2)CE & lt； Bulgaria

Proof: because DB=DC (proved)

So the triangle DBC is an isosceles triangle.

Because point h is the midpoint of BC

So DH is the middle vertical line of isosceles triangle.

So BG=CG

Because GEC angle =90 degrees (proven)

So in the right triangle GEC, the angle GEC=90 degrees.

So CG & gtCE (in a right triangle, the hypotenuse is larger than the right)

So ce