Question

prove that a cyclic quadrilateral is a rectangle

Answer 1

Heya mate,
Here is your answer


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.

<ABC = 90° and  < ADC = 90°

 Similarly, BD is a diameter.

  <DAB = 900  and  <BCD = 90°

  Therefore,  < ABC = <ADC = <DAB = <BCD = 90°

Thus, ABCD is a rectangle

Hope this helps

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Thank you

#Sneha
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Answer 2

Hyy

We know that ..

Each angle of a rectangle is a right angle.

Therefore ,

Sum of oppsite angles of a rectangle is supplementary i.e., 180°

For a cyclic quadrilateral, sum of opposite angles is 180°.

=> 90° + 90° = 180° ( sum of opposite angles of a rectangle ).

Hence, rectangle is a cyclic quadrilateral.

Thank you