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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 FalseGiven−PA&PBaretangentstothecirclewtthcentreOatA&Brespectively.Tofindout−Theassertion,PAorPBisalways>OAorOB,istrueorfalse.Justification−PA&PBaretangentstothecircleatA&Brespectively.∴PA=PBand∠OAP&∠OBPare=90o∴ΔOAPisarightonewith∠A=90o⟹∠AOP+∠APO=90o(byanglesumprqpertyoftriangles)caseI−∠AOP=∠APO⟹eachofthem=45o.i.ePA=OAcaseII−∠AOP>∠APO⟹∠AOP>45o&∠APO<45o(inaΔthesideoppositetothegreaterangleisgreaterthanthesideoppositetothesmallerangle)⟹PA>OAcaseIII−∠AOP<∠APO⟹∠AOP<45o&∠APO>45o(sameargumentascaseII)⟹PA>OASotheassertion,PAorPBisalways<OAorOB,isfalse.Ans−False.

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