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

Vedclass · Accepted Answer

$4.8$

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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 $\frac{AM}{MB} = \frac{4}{13}$,therefore $\frac{AN}{NC} = \frac{4}{13}$.Let $AN = 4x$ and $NC = 13x$.We know that $AC = AN + NC$.Substituting the values,$20.4 = 4x + 13x$.$20.4 = 17x$.$x = \frac{20.4}{17} = 1.2$.Now,$AN = 4x = 4 	imes 1.2 = 4.8$.

In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $AM : MB = 4 : 13$ and $AC = 20.4$,find $AN$.

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