The radius of a circle is 40 cm and the length of perpendicular drawn from its centre to chord is 24 cm. The length of chord is
A
32cm
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B
64cm
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C
8cm
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D
16cm
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Solution
The correct option is B 64cm Given−Oisthecentreofacircleofradius40cm.ABisachordofthegivencircleandABisatadistanceof24cmfromO.Tofindout−ThelengthofAB=?.Solution−WejoinOAanddropaperpendicularONtoAB.ONmeetsABatN.soOAistheradiusofthecircleandOA=40cm.AgainONistheperpendiculardroppedfromOtoABatN.∴ONistheperpendiculardistanceofABfromO.SoON=24cm&∠ONA=90o.∴ΔOANisarighttrianglewithOAashypotenuse.So,applyingPythagorastheorem,wegetAN=√OA2−ON2=√402−242cm=32cm.NowAB=2ANsincetheperpendicular,droppedfromthecentreofacircletoitsanychordbisectsthelatter.∴AB=2×32cm=64cm.Ans−OptionB.