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