In a triangle ABC, AD,BE,CF are the medians which intersect each other at G. To prove: GE =1/3 BE
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Answer:
BE is the median of ΔABC
so, ar(ΔBEC)=
2
1
ar(ΔABC) __(1)
Median of triangle divides into 2 triangles of equal area.
Also CF is median of ΔABC
⇒ar(ΔACF)=
2
1
ar(ΔABC) __(2)
from (1) and (2)
ar(ΔACF)=ar(ΔBEC)
ar(ΔGBC)+ar(ΔGEC)=ar(AFGE)+ar(GEC)
∴ar(ΔGBC)=ar(AFGE)
solution
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