We can add some lines to the picture:
We know that AC=DB, and AB and DC bisect each other.
The figure ACBD is a regular quadrilateral becuase the conditions above, AC=DB and AB and DC bisect each other.
The triangles AOC and DOB are similar because AC=DB and the other sides are equals too because AB and DC bisect each other, that means they cut in the middle of each one.
