Question

Prove that a cyclic rhombus is a square.

Answer 1

In figure ABCD is a rhombus in circle

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

$\angle A+\angle C={180}^0$ (Opposite angle of cyclic rhombus)

$\therefore \angle A+\angle A={180}^0$

$\Rightarrow \angle A={90}^0$

And $\angle B+\angle D={180}^0$ (Opposite angle of cyclic rhombus)

$\therefore \angle B+\angle B={180}^0$

$\Rightarrow \angle B={90}^0$

$\therefore \angle A=\angle B=\angle C=\angle D={90}^0$

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