Mathematics
In the figure (i) given below, AD is a diameter of a circle with center O. If AB || CD, prove that AB = CD.
Circles
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Answer
Draw OM ⊥ AB and ON ⊥ CD,
In △OAM and △ODN,
OA = OD (Radius of circle)
∠AOM = ∠DON (Vertically opposite angles are equal)
∠OMA = ∠OND (Both equal to 90°)
∴ △OAM ≅ △ODN (By A.S.A. axiom).
∴ ND = AM (By C.P.C.T.) ……..(1)
Since, the perpendicular to a chord from the centre of the circle bisects the chord,
so, equation 1 can be written as,
⇒
⇒ AB = CD.
Hence, proved that AB = CD.
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