In triangle $ABC$, let $I$ be the incenter of triangle $ABC$. The line through $I$ parallel to $BC$ intersects $AB$ and $AC$ at $M$ and $N$, respectively. If $AB = 5$, $AC = 5$, and $BC = 8$, then find the area of triangle $AMN$.
Find the area of triangle AMN.
¯AB=c=5,¯AC=b=5 and ¯BC=a=8
A=s(s−a)(s−b)(s−c) Heron′s formulas=a+b+c2=8+5+52=9AABC=9(9−8)(9−5)(9−5)AABC=144Any line through the center of gravity of a triangle divides it into equal parts.AAMN=12⋅AABC=12⋅144AAMN=72
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