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Question

If arcs AXB and CYD of a circle are congruent, find the ratio of AB and CD.

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Solution


Let AXB and CYD are arcs of a circle whose centre and radius are O and r units, respectively.
So, OA=OB=OC=OD=r......(i)
arc AXB arc CYD

AOB=COD [congruent arcs of a circle subtend equal angles at the centre].....(ii)

In ΔAOB and ΔCOD, we have

AO=CO [Radii]

BO=DO [Radii]

AOB=COD [from above eq.(ii)]

ΔAOBΔCOD [by SAS congruence rule]

AB=CD [by CPCT)

ABCD=1

Hence, the ratio of AB and CD is 1:1


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