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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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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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