Question

prove a cyclic parallelogram is a rectangle

Answer 1

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.

Hence ABCD is a rectangle.

Answer 2

ang.A=ang.D(ABCD is parrellogram)
Similarly ang.B=Ang.D
so,ABCD is a cyclic parallelogram
so,A+D=180
2A=180
A=90=D
Similarly B=D=90
so A=B=C=D
So,ABCD is a rectangle.
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