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Given: Consider any AARC, with eevians AD, BM, CF eoneurrent at B. Let 5' denote the area of AARC and $1, $2, 53, S4, 55, 55 denote the areas of the...

Prove: If the area(ABC)=2(S1+S3+S5), then point M must be the midpoint of AC, or i.e. point E lies on the median BM.


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Given: Consider any AARC, with eevians AD, BM, CF eoneurrent at B.
Let 5' denote the area of AARC and $1, $2, 53, S4, 55, 55 denote the areas of the smaller triangles inside MEG (refer to picture). Prove: If S = 2(51 + 53 + $5) = 2(52 —E— 5,; + 55), then M must be the midpoint ofAC (i.e. point E lies on the median BM) Given:
. MBC AD. BH.CF maetaE
8=araaaABC
S1=areaAEAF
Sa=areaAEFB
Sq=areaAEBD
St=areaAEDc
Ss=areaAECM
3.:areaAEHA I
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