Mathematics
In the figure (ii) given below, two equal chords AB and CD of a circle with center O intersect at right angles at P. If M and N are mid-points of the chords AB and CD respectively, prove that NOMP is a square.
Circles
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Answer
In NOMP,
∠P = 90° (As chords intersect at right angles)
∠M = ∠N = 90° (Straight lines from center bisecting the chord are perpendicular to it.)
∠O = 360° - (∠M + ∠N + ∠P)
= 360° - (90° + 90° + 90°)
= 90°
Since, equal chords are equidistant from center,
∴ OM = ON.
Since, all angles = 90° and all sides are equal.
Hence, NOMP is a square.
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