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Q.

In Δ ABC, If D, E, F are the Midpoints of the sides BC, CA, AB. Also G is its centriod, S is circum centre H is orthocentre then Match the following lists

 List - I List - II
I)AD + BE + CFa)GS
II)HGb)O
III)OD + OE + OFc)12 AC
IV)AD + 23BE + 13CFd)OG
  e)23 HS

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a

I-b, II-e, III-a, IV-c

b

I-b, II-e, III-d, IV-c

c

I-b, II-a, III-d, IV-a

d

I-b, II-a, III-d, IV-b

answer is B.

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Detailed Solution

OA=a            OB=b          OC=c OD=b+c2   OE=c+a2   OF=a+b2 I)    AC+BE+CF=b+c2-a+c+a2-b+a+b2-c II)   2:1H        4        S HG=23 HS III)   OD+OE+OF=a+b+c=3(0G) IV)  AD+23(BE)+13CF       =b+c2-a+c+a3-23b+13a+b2-c=12AC

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