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Question

Draw different pairs of circles. How many points does each pair have in common ? The maximum number of common point/points is/are

A
2
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B
1
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C
infinite
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D
0
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Solution

The correct option is C infinite
SolutionWedrawpairsofcirclessothat(i)Thedistancebetweenthecentres>thesumoftheirradii,(ii)Thedistancebetweenthecentres=thesumoftheirradii,(ii)Thedistancebetweenthecentres<thesumoftheirradii,(ii)Thedistancebetweenthecentres=0Take(a)differetradii(b)equalradii.InfigIThedistancebetweenthecentres>thesumoftheirradii,Nocommonpoint.InfigIIThedistancebetweenthecentres=thesumoftheirradii,Onecommonpoint.InfigIIIThedistancebetweenthecentres<thesumoftheirradii,Twocommonpoints.InfigIVaThedistancebetweenthecentres=0andtheradiiaredifferent.Nocommonpoint.InfigIVbThedistancebetweenthecentres=0andradiiareequal.Thecircleswillcoincide.Infinitenumberofcommonpoints.AnsOptionC,
286453_242974_ans.png

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