In Delta ABC,M lies on AB and N lies on AC su | vedclass

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(A) According to the Basic Proportionality Theorem (Thales Theorem),if a line is drawn parallel to one side of a triangle to intersect the other two s

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$20$

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(A) According to the Basic Proportionality Theorem (Thales Theorem),if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points,then the other two sides are divided in the same ratio.Since $\overline{MN} \parallel \overline{BC}$,we have:$\frac{AM}{MB} = \frac{AN}{NC}$Given $AM = 6$,$MB = 9$,and $AN = 8$,we substitute these values:$\frac{6}{9} = \frac{8}{NC}$$\frac{2}{3} = \frac{8}{NC}$$2 	imes NC = 8 	imes 3$$2 	imes NC = 24$$NC = 12$Since $AC = AN + NC$,we have:$AC = 8 + 12 = 20$.

In $\Delta ABC$,$M$ lies on $AB$ and $N$ lies on $AC$ such that $\overline{MN} \parallel \overline{BC}$. If $AM = 6$,$MB = 9$,and $AN = 8$,find $AC$.

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