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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.
The diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral.
We have to prove that it is a rectangle.
Let $PR$ and $QS$ be the diagonals of a cyclic quadrilateral $PQRS$.
$PR$ and $QS$ are diameters of the circle.
$OP=OQ=OR=OS$ (Radii of the circle)
The diagonals of the quadrilateral $PQRS$ are equal and bisect each other.
Therefore, quadrilateral $PQRS$ is a rectangle.
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