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If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.

Q: 7     If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.

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M mansi

AC is the diameter of the circle.

Thus,\angle ADC=90 \degree   and    \angle ABC=90 \degree............................1(Angle in a semi-circle is right angle)

Similarly, BD is the diameter of the circle.

 Thus,\angle BAD=90 \degree   and    \angle BCD=90 \degree............................2(Angle in a semi-circle is right angle)

From 1 and 2, we get

          \angle BCD=\angle ADC=\angle ABC=\angle BAD =90 \degree

Hence, ABCD is a rectangle.

 

 

 

 

 

 

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