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Answer :
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 = (\(\frac{1}{2} \) ) NP
and OM = OQ = (\(\frac{1}{2} \) ) MQ
\(\therefore \) NP = MQ
Hence, the diagonals MPQN are equal and bisect each other.
Hence, it is proved that quadrilateral NQPM is a rectangle.