Question

Prove that the centre of the circle circumscribing the cyclic rectangle ABCD is the point of intersection of its diagonals.

Answer 1

Given: ABCD is a cyclic rectangle and diagonals AC and BD intersect each other at O.

To prove: O, the point of intersection of the diagonals, is the centre of the circle.

Proof: Let O be the centre of the circle circumscribing the rectangle ABCD. Since each angle of a rectangle is a right angle and AC is the chord of the circle, AC will be the diameter of the circle. Similarly, we can prove that diagonal BD is also the diameter of the circle.

$\because$ The diameters of a circle pass through the centre, the point of intersection of the diagonals of the rectangle is the centre of the circle.