If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.
Let ABCD be a cyclic quadrilateral having diagonals BD and AC, intersecting each other at point O which is centre of the circle.
Consider, ΔABC,as AC is the diameter, therefore,
⇒∠ABC=90∘ (Angle in a semi circle is 90∘)
Consider, ΔBCD,as DB is the diameter, therefore,
⇒∠DCB=90∘ (Angle in a semi circle is 90∘)
Since, ABCD be a cyclic quadrilateral, therefore,
Since, all the angles of cyclic quadrilateral ABCD are 90∘, therefore,
ABCD is a rectangle.