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 having diagonals BD and AC, intersecting each other at point O.

∠ADC + ∠ABC = 180° (Cyclic quadrilateral)

90° + ∠ABC = 180°

∠ABC = 90°

Each interior angle of a cyclic quadrilateral is of 90°. Hence, it is a rectangle.