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Question

For a circle which is inscribed in a Δ ABC having sides 8 cm, 10 cm and 12 cm (figure), match the columns.
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A
A1B4C3D2
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B
A2B3C4D1
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C
A1B2C3D4
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D
A4B2C3D1
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Solution

The correct option is B A2B3C4D1
Applytheconceptthatthelengthofthetwotangents,drawnfromapointtoacircle,areequal.
GivenABCisaΔanditsincircletouchesthesidesAB,BC&ACatD,E&Frespectively.AB=12cm,BC=8cm&AC=10cm.TofindoutthevaluesofAD,BE,CFandADAF=?SolutionHereweusetheconceptthatthelengthofthetwotangents,drawnfromapointtoacircle,areequal......(i).LetAD=xcm.........(ii).thenBD=ABAD=12x........(iii).So,by(i)BE=BD=12x.......(iv).Also,by(i)AF=AD=x.......(v).CF=ACAF=10x.......(vi).i.eby(i)CE=CF=10x.SoBE=BCCE=8(10x)=x2......(vii).Again,by(i)BD=BE=x2.......(viii).Now,bycomparing(iii)&(viii),wehave12x=x2x=7.Substitutingx=7in(ii),(iv)&(vi)wehaveAD=x=7cm,BE=12x=(127)cm=5cmandCF=10x=(107)cm=3cmandfrom(v)ADAF=xx=1.SothereqiredmatchingsareA2B3C4D1AnsOptionB

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