Question

If a parallelogram is cyclic, then it is a rectangle. Justify.

Answer 1

The ABCD is a cyclic parallelogram

Then $\angle A=\angle C$ (Opposite angle of parallelogram )

In cyclic parallelogram ABCD

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

$\Rightarrow 2\angle A={180}^0$

$\Rightarrow \angle A=\frac{180}{2}={90}^0$

And $\angle B=\angle D$ (Opposite angle of parallelogram )

In cyclic parallelogram ABCD

$\angle B+\angle D={180}^0$ (Sum of Opposite angle of cyclic parallelogram=180 degree )

$\Rightarrow 2\angle B={180}^0$

$\Rightarrow \angle B=\frac{180}{2}={90}^0$

So in parallelogram ABCD all angle are right angle then ABCD is a rectangle