Question

prove that cyclic parallelogram is a rectangle​

Answer 1

Given :- ABCD is a Cyclic Parallelogram

To prove :- ABCD is a rectangle

To Proof:- ∠1 + ∠2 = 180° ---(Opposite Angles of a cyclic parallelogram)

Also, Opposite angles of a cyclic parallelogram are equal.

Thus,

∠1 = ∠2

∠1 + ∠1 = 180°

=> ∠1 = 90°

One of the interior angle of the parallelogram is right angled. Thus,

ABCD is a rectangle

Answer 2

Given : ABCD is a cyclic parallelogram inside circle

To Prove: Cyclic parallelogram is a rectangle.

Proof : In parallelogram ABCD

$\small\implies{\sf }$ ∠BDC + ∠BAC = 180° ...( As we know that sum of opposite angles of a cyclic parallelogram is 180° and also these opposite angles are equal to each other)

Therefore,

$\small\implies{\sf }$ ∠BDC = ∠BAC = 180°

$\small\implies{\sf }$ 2∠BDC = 180°

$\small\implies{\sf }$ ∠BDC = 180/2 = 90°

Hence, ∠BDC = ∠BAC = 90°

similarly ∠ACD = ∠ABD = 90°

So, It is also a Rectangle