Constructing a single ray, divide a line segment of length 12 cm in the ratio 6:3.

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Solution

In the figure, $A A_{1} = A_{1} A_{2} = . . . . . . = A_{8} A_{9}$ and so on.
Join $A_{9}$ and B. Draw a line parallel to $A_{9} B$ from $A_{6}$ .
The point where this line from $A_{6}$ intersects the line segment AB is the required point C which divides the line segment AB in the ratio of 6:3

Note: The line segment can also be divided in the same ratio by dividing it in the ratio 2:1 as 6:3

Hence, $\frac{A C}{B C}$ = $\frac{6}{3}$ or $\frac{2}{1}$ .

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