Question

Prove that a cyclic rhombus is a square

Answer 1

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GIVEN- Rhombus ABCD is inscribed in a circle .

TO PROVE- ABCD is a square.

Answer 2

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

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