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Question

Write True or False and justify your answer in each of the following :

The length of tangent from an external point P on a circle with centre O is always less than OP.

A
True
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B
False
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C
Data insufficient
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D
Ambiguous
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Solution

The correct option is B False
GivenPA&PBaretangentstothecirclewtthcentreOatA&Brespectively.TofindoutTheassertion,PAorPBisalways>OAorOB,istrueorfalse.JustificationPA&PBaretangentstothecircleatA&Brespectively.PA=PBandOAP&OBPare=90oΔOAPisarightonewithA=90oAOP+APO=90o(byanglesumprqpertyoftriangles)caseIAOP=APOeachofthem=45o.i.ePA=OAcaseIIAOP>APOAOP>45o&APO<45o(inaΔthesideoppositetothegreaterangleisgreaterthanthesideoppositetothesmallerangle)PA>OAcaseIIIAOP<APOAOP<45o&APO>45o(sameargumentascaseII)PA>OASotheassertion,PAorPBisalways<OAorOB,isfalse.AnsFalse.

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