Question

prove that a cyclic parallelogram is a rectangle

Answer 1

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Let ABCD be a cyclic quadrilateral such that its diagonals AC and BD are the diameters of the circle through the vertices A, B, C, and D.

 Since AC is a diameter and angle in a semi-circle is a right angle, 

angle ADC = 900 and angle ABC = 900

 Similarly, BD is a diameter. 

Therefore, angle BCD = 900 and angle BAD = 900

Thus, ABCD is a rectangle
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Answer 2

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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.☺

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