Question

prove that a cyclic parallelogram is a rectangle

Answer 1

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 

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Answer 2

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