properities of circle

11)
Link up B and E.
angle ABE=90
angle CBE+angle CDE=180 (Opp. angles , cyclic quad.)
So, angle ABC+angle CDE
=angle ABE+angle CBE+angle CDE
=90+180
=270

12a)
In tri ABC and tri ADC,
AB=AD (Given)
BC=DC (Given)
AC=AC (Common side)
tri ABC ≅ tri ADC (S.S.S.)

b)
Since tri ABC ≅ tri ADC
angle ABC=angle ADC
angle ABC+angle ADC=180 (Opp. angles , cyclic quad.)
2*angle ABC=180
angle ABC=angle ADC=90
Hence, AC is a diameter of the circle.

c)
If angle BAD=angle BCD=90,
i.e. AB=BC=CD=DA, then BD can be a diameter.