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 bothQuote:

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

Angles ADC and ABC either have to be right angled, or summing to

Having them sum to is required.