Question

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

Answer 1

Let $ABCD$ be a cyclic quadrilateral and its diagonal $AC$ and $BD$ are the diameters of the circle through the vertices of the quadrilateral.

$\angle ABC=\angle BCD=\angle CDA=\angle DAB=90°$ ...Angles in the semi-circle

Thus, $ABCD$ is a rectangle as each internal angle is $90°$