Mathematics
In the figure (ii) given below, chords AB and CD of a circle with centre O intersect at E. If OE bisects ∠AED, prove that AB = CD.
Circles
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Answer
Draw perpendiculars from O to AB and CD.
In △OME and △ONE,
∠OME = ∠ONE = 90°
∠OEM = ∠OEN (As OE bisects ∠AED)
OE = OE (Common side)
∴ △OME ≅ △ONE (By A.A.S. axiom)
∴ OM = ON (By C.P.C.T.C.)
Hence, chords AB and CD are equidistant from the center of circle.
In the same circle, chords equidistant from the centre are equal.
∴ AB = CD.
Hence, proved that AB = CD.
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