Question

prove that a cyclic Parallelogram is a rectangle

Answer 1

Let the opposite angles be a and b

We know that opposite angles of paralellogram are equal..

a = b -----(1)

And opposite angles of cyclic quadrilateral are suplementry....

a +b =180

=> a +a = 180

=> 2a = 180

=> a = 90°

Opposite angles are 90°

And we know that a paralellogram whose one angle is 90° is a rectangle....

Answer 2

Let ABCD is a parallelogram inscribed in circle.

Since ABCD is a cyclic parallelogram, then

∠A + ∠C = 180 ....1

But ∠A = ∠C

So ∠A = ∠C = 90

Again

∠B + ∠D = 180 ....2

But ∠B = ∠D

So ∠B = ∠D = 90

Now each angle of parallelogram ABCD is 90.

Hense ABCD is a rectangle.