if a parallelogram is cyclic, then it is a rectangle? justify
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yes, it is because if the cyclic is parallelogram then it's opposite angles will be equal. and as we know sum of opposite angles in a cyclic is 180°. hence as angle 1 = angle 2 then angle 1=90°
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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.
As, AC is a diameter and angle in a semi-circle is a right angle
⇒∠ADC = 90 and ∠ABC = 90
Similarly,
BD is a diameter.
⇒∠BCD = 90 and ∠BAD = 90
Thus, ABCD is a rectangle
through the vertices A, B, C, and D.
As, AC is a diameter and angle in a semi-circle is a right angle
⇒∠ADC = 90 and ∠ABC = 90
Similarly,
BD is a diameter.
⇒∠BCD = 90 and ∠BAD = 90
Thus, ABCD is a rectangle
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