Question

proove that cyclic rhombus is a square

Answer 1

we know that a cyclic quadrilateral has sum of its opposite angles as 180°
so if there is a rhombus ABCD then A+C=180 , B+D=180
now a rhombus is a parallelogram and a parallelogram has its opposite angles and sides equal
so A=C , B=D
now A+C=180
Now since A=C so. A+A=180. 2A=180. A=90
Now we know that
if a quadrilateral has all its sides equal and angles equal to 90 then it is a square
so ABCD is a square. hence proven