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CBSE Class 9 Answered

AB and CD are two parallel chords of a circle whose diameter is AC, prove that AB = CD.
Asked by Topperlearning User | 18 Aug, 2017, 09:03: AM
answered-by-expert Expert Answer
Construction: Draw OL ⏊ AB and OM ⏊ CD.

As OL⏊AB and OM⏊CD, we get L – O – M.

∴ LM is a straight line.

Then, AB||CD and AC is a transversal.

∴ begin mathsize 10px style angle end styleOAL = begin mathsize 10px style angle end styleOCM       (∵ alternate angles)

In Δ OLA and ΔOMC,

begin mathsize 10px style angle end styleOLA = begin mathsize 10px style angle end styleOMA         (∵ right angles)

begin mathsize 10px style angle end styleOAL = begin mathsize 10px style angle end styleOCM

OA = OC                             (∵ radii of same circle)

Therefore, ΔOLA begin mathsize 10px style approximately equal to end style ΔOMC       (∵ by ASA property)

rightwards double arrowAL = CM                        (corr. parts of cong. triangles)

rightwards double arrow2AL = 2CM

rightwards double arrowAB = CD                       (perpendicular from the centre bisects the chord)

Answered by | 18 Aug, 2017, 11:03: AM

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