If two arcs of a circle (or of congruent circles) are congruent, then
corresponding chords are equal.
Text Solution
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Let AXB and CYD are arcs of circle whose centre and radus are O and r units, respectively. So, OA=OB=OC=OD=r …..(i) `:' "arc "AXB cong"arc "CYD` ` :. angle AOB=angleCOD ` [congruent arcs of a circle subtend equal angles at the centre] In `DeltaAOB abd DeltaCOD`, AO=CO [form Eq. (i)] BO=DO [from Eq.(i)] `angle AOB=angleCOD` [from Eq. (ii)] `:.Delta AOB cong Delta COD`[by SAS songruence rule] `rArr AB=CD` [by COCT] `rArr (AB)/(CD)=1` the ratio of AB and CD is `1 : 1`.
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