Question

prove that a cyclic rhombus is a square.
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Answer 1

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Answer 2

Let ABCD be a cyclic parallelogram

Angle A= Angle C (opposite angles of a parallelogram)
Angle A+Angle C=180 (opposite angles of a cyclic quadrilateral are supplementary)
i.e. 2(angle A)=180 ( angle A=angle C)
angle A=180/2 = 90
Similarly, Angle B=Angle D (opposite angles of a parallelogram)
Angle B+Angle D= 180 (opposite angles of a cyclic quadrilateral are supplementary)
Since,all four angles are 90 ABCD is a rectangle 
i.e. a cyclic parallelogram is a square
HENCE PROVED !

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