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Question

Prove that a cyclic rhombus is a square.

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Solution

In figure ABCD is a rhombus in circle

A+C and B+D ( Opposite angle of rhombus is Equal)

A+C=1800 (Opposite angle of cyclic rhombus)

A+A=1800

A=900

And B+D=1800 (Opposite angle of cyclic rhombus)

B+B=1800

B=900

A=B=C=D=900

Then all angle of rhombus is right angle then this is a square



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