Mathematics
In the adjoining figure, BC is a diameter of a circle with centre O. If AB and CD are two chords such that AB ∥ CD, prove that AB = CD.
Answer
Draw LM through O perpendicular to AB and CD.
In △ OLB and △ OMC :
OB = OC [radii of same circle]
∠OLB = ∠OMC = 90°
∠OBL = ∠OCM [Alternate interior angles are equal]
∴ △ OLB ≅ △ OMC [By A.A.S. axiom]
Since the triangles are congruent, their corresponding parts are equal.
OL = OM
Chords equidistant from the center of a circle are equal in length.
∴ AB = CD.
Hence, proved that AB = CD.
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