Question

Prove that a cyclic parallelogram is always a rectangle

Answer 1

in a cyclic quadrilateral, the sum of opposite angles is always 180 degrees. so, in a cyclic parallelogram the sum of opposite angles will also be 180 degrees. since the opposite angles of a parallelogram are equal,
angle a + angle c = 180
angle a + angle a =  180   (because angle a = angle c)
angle a = 180/2 = 90 degrees.

so, angle a = angle c = 90 degrees 

similarly angle b and angle d is also 90 degrees.

since all the angles will become 90 degrees,every cyclic parallelogram is always a rectangle

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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