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 intersecting the other two s

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$4$

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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 intersecting the other two sides,then it divides the two sides in the same ratio.Given $\overline{MN} \parallel \overline{BC}$,we have:$\frac{AM}{MB} = \frac{AN}{NC}$Substituting the given values:$\frac{x}{x-2} = \frac{x+2}{x-1}$Cross-multiplying gives:$x(x-1) = (x-2)(x+2)$$x^2 - x = x^2 - 4$Subtracting $x^2$ from both sides:$-x = -4$$x = 4$Therefore,the value of $x$ is $4$.

In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $AM = x$,$MB = x-2$,$AN = x+2$ and $NC = x-1$,find the value of $x$.

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