Question

prove that the cyclic rhombus is a square​

Answer 1

We know that a rhombus is a parallelogram and a parallelogram has its opposite sides equal

so in a rhombus ABCD A=C and B=D

now given ABCD is a cyclic quadrilateral

and a cyclic quadrilateral has its opposite sides sum as 180

so

A+C=180

since A=C so

A+A=180

A=90Now if a rhombus has one of its angles as90 then it's a square

so ABCD is a square