Prove that a cyclic parallelogram is a rectangle.
.Q. Prove that a cyclic parallelogram is a rectangle ?
ANS : 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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