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prove that of all chords of circle through a given point within it, the chord which is bisected at that point is the smallest
Asked by subbusuchi1978 | 05 Nov, 2023, 10:24: AM
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Figure shows a circle of radius R .  Let AB and CD are chords that is passing through a point E .

Chord AB is bisected at E . Chord CD is not bisected at E.

Perpendicular distance h1 to the chord AB  is greater than perpendicular distance h2 to the chord CD .

Length of chord AB

Length of chord CD
Since h1 > h2 ,  we get AB < CD

Hence , if many chords are passing through a common point within a circle ,
then length of chord that is bisected by the common point has smallest length

Answered by Thiyagarajan K | 05 Nov, 2023, 11:48: AM

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