Question

Prove that a cyclic Parallelogram is a rectangle

Answer 1

Answer

Let ABCD be a cyclic Parallelogram 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

A cyclic parallelogram means that

sum of opposite angles of a llgm is 180°

So here,

In a rectangle, all angles are 90°

One pair of opposite angles of rectangle will have 90° each .

sum of these opposite angles will be 90 +90=180° .

Hence proved...