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. 

Ex:3 Cyclic quadrilaterals  

 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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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.

Ex:3 Cyclic quadrilaterals

 <ABC = 900  and  < ADC = 900

 Similarly, BD is a diameter.

  <DAB = 90 and  <BCD = 900

  Therefore,  < ABC = <ADC = <DAB = <BCD = 900

Thus, ABCD is a rectangle

 
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