Question

prove that cyclic quadrilateral is a rectangle

Answer 1

hey dude .....
ur answer is here........!!!!!!!!

for diagram draw a circle then draw the quadrilateral same like rectangle and mark any two angles any two opposite to each other and mark them angle 1 & 2.

Given:
ABCD is a cyclic parallelogram.
To Prove:
ABCD is a rectangle.

Proof:
∵ ABCD is a cyclic quadrilateral
∴ ∠1 + ∠2 = 180° ...(1)
| ∵ Opposite angles of a cyclic

quadrilateral are supplementary
∴ ABCD is a parallelogram
∴ ∠1 = ∠2 ...(2)
| Opp. angles of a ||gm

therefore,,
From (1) and (2),
∠1 = ∠2 = 90°

∴ || gm ABCD is a rectangle.



thanks.....!

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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