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Question

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
GivenOisthecentreofacircleofradius40cm.ABisachordofthegivencircleandABisatadistanceof24cmfromO.TofindoutThelengthofAB=?.SolutionWejoinOAanddropaperpendicularONtoAB.ONmeetsABatN.soOAistheradiusofthecircleandOA=40cm.AgainONistheperpendiculardroppedfromOtoABatN.ONistheperpendiculardistanceofABfromO.SoON=24cm&ONA=90o.ΔOANisarighttrianglewithOAashypotenuse.So,applyingPythagorastheorem,wegetAN=OA2ON2=402242cm=32cm.NowAB=2ANsincetheperpendicular,droppedfromthecentreofacircletoitsanychordbisectsthelatter.AB=2×32cm=64cm.AnsOptionB.
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