A line segment AB is divided in the ratio 4:9 by a point C. Find the length AC (in cm) if AB=26 cm.

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Solution

$\frac{A C}{B C}$ = $\frac{4}{9}$

Therefore, $\frac{A B}{A C}$ = $\frac{A C}{A C}$ + $\frac{B C}{A C}$ = $1$ + $\frac{9}{4}$ = $\frac{13}{4}$

$\frac{A C}{A B}$ = $\frac{4}{13}$ . So, $A C = A B$ $\times$ $\frac{4}{13}$ = $8 c m$

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