Draw a line segment $\overline{AB}$ of length $8\, cm$ and divide it in the ratio $2:3:5$ starting from point $A$. Write the steps of construction.
(N/A) Step $1$: Draw a line segment $\overline{AB} = 8\, cm$ using a ruler.
Step $2$: Draw an acute angle $\angle BAX$ at point $A$ with the line segment $\overline{AB}$.
Step $3$: Mark $2 + 3 + 5 = 10$ points $A_1, A_2, A_3, \dots, A_{10}$ on the ray $AX$ such that $AA_1 = A_1A_2 = A_2A_3 = \dots = A_9A_{10}$ using a compass.
Step $4$: Join the last point $A_{10}$ to point $B$.
Step $5$: Through points $A_2$ and $A_5$ (since $2$ and $2+3=5$),draw lines parallel to $A_{10}B$ intersecting $\overline{AB}$ at points $P$ and $Q$ respectively.
Step $6$: The points $P$ and $Q$ divide the line segment $\overline{AB}$ in the ratio $2:3:5$.
Step $2$: Draw an acute angle $\angle BAX$ at point $A$ with the line segment $\overline{AB}$.
Step $3$: Mark $2 + 3 + 5 = 10$ points $A_1, A_2, A_3, \dots, A_{10}$ on the ray $AX$ such that $AA_1 = A_1A_2 = A_2A_3 = \dots = A_9A_{10}$ using a compass.
Step $4$: Join the last point $A_{10}$ to point $B$.
Step $5$: Through points $A_2$ and $A_5$ (since $2$ and $2+3=5$),draw lines parallel to $A_{10}B$ intersecting $\overline{AB}$ at points $P$ and $Q$ respectively.
Step $6$: The points $P$ and $Q$ divide the line segment $\overline{AB}$ in the ratio $2:3:5$.
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