This is the specific case when angles ADC and ABC are right angles.
Again, those triangles would be right angled.Quote:
OR
AC divides BD into 2 equal parts
Those angles being equal can have the angles ADC and ABC both $\displaystyle >90^o$Quote:
OR
The angels ACB and ACD are equal ?
in which case the quadrilateral would not be cyclic,
since opposite angles would not necessarily sum to $\displaystyle 180^o$
Angles ADC and ABC either have to be right angled, or summing to $\displaystyle 180^o$
Having them sum to $\displaystyle 180^o$ is required.