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Question 12
Prove that a cyclic parallelogram is a rectangle.


Solution


Let ABCD be a cyclic parallelogram.
A+C=180 (Opposite angles of a cyclic quadrilateral) 
We know that opposite angles of a parallelogram are equal.
A=C and B=D 
A+C=180
Then A+A=180
2A=180
A=C=90
Parallelogram ABCD has one of its interior angles as 90. Therefore, it is a rectangle.

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