In Delta ABC,A-M-B,A-N-C and overline{MN} par | vedclass

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(C) 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

Vedclass · Accepted Answer

$24$

Vedclass · Answer

(C) 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 $AM = 6$,$MB = 12$,and $AN = 8$,we substitute these values into the equation:$\frac{6}{12} = \frac{8}{NC}$$\frac{1}{2} = \frac{8}{NC}$$NC = 8 	imes 2 = 16$Since $A-N-C$,we have $AC = AN + NC$.$AC = 8 + 16 = 24$.

In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $AM = 6$,$MB = 12$ and $AN = 8$,find $AC$.

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