Question

a cyclic quad whose diagonals bisect each other at 90 is a square.​

Answer 1

Let ABCD be the quad.
since diagonals diagonals bisect each other at 90 is a rhombus

angle ABC= angle CDA
as we know ,
sum of opposite angles becomes 180
angleABC+angleCDA=180
2angle ABC=180
angle ABC=90
SO,ABCD is a square
all angles 90