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Two circle od radii 26 cm and 10 cm are concentric.Find the length of a chord of the outer circle which touches the inner​

Answer»

-step EXPLANATION:AnswerGiven−OisthecentreoftwoconcentriccirclesandAB,whichisachordoftheoutercircle,touchestheinnercircleatP.Theradiusoftheinnercircleis10cmandtheradiusoftheoutercircleis26cm.Tofindout−thelengthofAB=?Solution−WejoinOP.ThenOPisaradiusthroughPwhichisthepointofcontactofABtotheinnercircle.i.ePO=10cm.AlsowejoinOA.ThenOAistheradiusoftheoutercircle=26cm.NowOP⊥AB⟹∠OPA=90 o sincetheradiusofacirclethroughthepointofcontactofatangenttothecircleisperpediculartothetangent.∴ΔOPAisarightonewithOAashypotenuse.So,applyingPythagorastheorem,AP= OA 2 −OP 2 = 26 2 −10 2 cm=24cmButAB=2APsincetheperpendicular,droppedfromthecenterofacircletoanyofitschord,bisectsthelatter.i.ePisthemidpointofAB.∴AB=2×24cm=48cm.



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