Question

12. Prove that a cyclic parallelogram is a rectangle.​

Answer 1

Answer:

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. 

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

 

⇒∠ADC = 900 and ∠ABC = 900

 

Similarly, 

BD is a diameter. 

⇒∠BCD = 900 and ∠BAD = 900

Thus, ABCD is a rectangle 

this is your answer

Answer 2

Answer:

Yes, cyclic parallelogram is a rectangle.

Step-by-step explanation:

Given:

• Let ABCD is a cyclic parallelogram.

To Prove:

• ABCD is a rectangle.

Proof:

⇒ ABCD is parallelogram, So, ∠ABC = ∠CDA  

(opposite angles of parallelogram are equal)

⇒ ∠ABC + ∠CDA = 180°  [ABCD is a cyclic parallelogram]

⇒ ∠ABC + ∠ABC = 180°             [∠ABC = ∠CDA]

⇒ 2∠ABC = 180°

⇒ ∠ABC = 90°

So, ∠ABC = ∠CDA = 90°

Similarly, ∠DAB = ∠BCD = 90°

We know that all angles of a rectangle is 90°. Hence it is a rectangle.

Hence Proved!!!

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