Given: Diagonals NP and QM of a cyclic quadrilateral are diameters of the circle
through the vertices M, P, Q and N of the quadrilateral NQPM.
To prove: Quadrilateral NQPM is a rectangle.
Proof: ON = OP = OQ = OM ...(Radii of circle)
Now, ON = OP = (1/2) NP
and OM = OQ = (1/2) MQ
Therefore, NP = MQ
Hence, the diagonals MPQN are equal and bisect each other.
Hence, it is proved that quadrilateral NQPM is a rectangle.