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Equal Chords of a Circle
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Equal Chords of a Circle
Theorem: Chords of a circle which are equidistant from the center are equal.
Chords are equidistant from the center if and only if their lengths are equal.
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Example: if two chords of a circle are equally inclined to the diameter through their point of intersection, prove that the chords are equal.
Solution: Two chords AB and AC of a circle C (O, r) such that AB and AC are equally inclined to diameter AOD.
TO PROVE AB = AC
Equal chords of a Circle

CONSTRUCTION Draw OL AB and OM AC.
PROOF In OLA and OMA, you have
OLA = OMA                    [each equal to 90]
OA = OA                               [common]
and,  OAL = OAM           [Given]
OLA OMA                   [by AAS congruence] 
OL = OM
Chords AB and AC are equidistant from O 
AB = CD.

 
   
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