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