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

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(D) 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

$9$

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(D) 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.Given $\overline{MN} \parallel \overline{BC}$,we have:$\frac{AM}{MB} = \frac{AN}{NC} = \frac{3}{4}$.Let $AN = 3x$ and $NC = 4x$.We know that $AC = AN + NC = 21$.Substituting the values,we get $3x + 4x = 21$,which implies $7x = 21$,so $x = 3$.Therefore,$AN = 3x = 3 	imes 3 = 9$.

In $\Delta ABC$,$M$ lies on $AB$ and $N$ lies on $AC$ such that $\overline{MN} \parallel \overline{BC}$. If $\frac{AM}{MB} = \frac{3}{4}$ and $AC = 21$,find $AN$.

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