To divide a line segment AB in the ratio 5: 6 | vedclass

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(A) To divide a line segment $AB$ in the ratio $m: n$ (here $5: 6$),we follow these steps:$1$. Draw a ray $AX$ making an acute angle $\angle BAX$ with

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$A_{5}$ and $B_{6}$

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(A) To divide a line segment $AB$ in the ratio $m: n$ (here $5: 6$),we follow these steps:$1$. Draw a ray $AX$ making an acute angle $\angle BAX$ with $AB$.$2$. Draw a ray $BY$ parallel to $AX$ by making $\angle ABY = \angle BAX$.$3$. Locate $m$ points $(A_{1}, A_{2}, \ldots, A_{5})$ on $AX$ and $n$ points $(B_{1}, B_{2}, \ldots, B_{6})$ on $BY$ such that $AA_{1} = A_{1}A_{2} = \ldots = A_{4}A_{5}$ and $BB_{1} = B_{1}B_{2} = \ldots = B_{5}B_{6}$.$4$. Join the point $A_{m}$ (which is $A_{5}$) to the point $B_{n}$ (which is $B_{6}$). The line segment $A_{5}B_{6}$ intersects $AB$ at point $C$,dividing $AB$ in the ratio $5: 6$.

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