Question

prove that a cyclic pallelogram is a rectangle

Answer 1

Any parallelogram cannot be cyclic. For any quadrilateral to be cyclic the sum of the opposite angles should be 180 deg. and. you answer is. If ABCD paralelogram is cyclic, then AB and CD are parallel chords of the circle. The orthogonal bisectors of chords go through the center of the circle, so the orthogonal bisector of AB and CD both should go through the center of the circle, but if ABCD is not a rectangle these bisectors are parallel lines and don’t go through the same point.

On the other hand rectangles are always cyclic, the vertices being the same distance from the intersection of the diagonals

Answer 2

Hello mate ☺

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Solution:

➡It is given that parallelogram ABCD is cyclic. We need to prove that ABCD is a rectangle.

∠B=∠D   (Opposite angles of a parallelogram are equal) ....(1)

∠B+∠D=180°   ...... (2)  

(Sum of opposite angles of a cyclic quadrilateral is equal to 180°)                    

Using equation (1) in equation (2), we get

∠B+∠B=180°

⇒2∠B=180°

⇒∠B=180/2=90°      …...(3)

➡Therefore, ABCD is a parallelogram with ∠B=90° which means that ABCD is a rectangle.

I hope, this will help you.☺

Thank you______❤

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