To divide a line segment $AB$ in the ratio $p: q$ ($p, q$ are positive integers),draw a ray $AX$ so that $\angle BAX$ is an acute angle and then mark points on ray $AX$ at equal distances such that the minimum number of these points is

To divide a line segment $AB$ in the ratio $5: 6,$ draw a ray $AX$ such that $\angle BAX$ is an acute angle,then draw a ray $BY$ parallel to $AX$ and the points $A_{1}, A_{2}, A_{3}, \ldots$ and $B_{1}, B_{2}, B_{3}, \ldots$ are located at equal distances on ray $AX$ and $BY,$ respectively. Then the points joined are

Draw $\odot(P, 5 \,cm)$ and take point $A$ in its exterior such that $PA = 9 \,cm$. Through $A$,draw a pair of tangents to $\odot(P, 5 \,cm)$. Write the steps of construction.

To divide a line segment $AB$ in the ratio $4:7,$ a ray $AX$ is drawn first such that $\angle BAX$ is an acute angle and then points $A_1, A_2, A_3, \dots$ are located at equal distances on the ray $AX$ and the point $B$ is joined to:

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.

Construct $\Delta ABC$ with $AB = 3 \, cm$,$BC = 6 \, cm$,and $AC = 5 \, cm$. Then,construct $\Delta BPQ$ similar to $\Delta ABC$ such that each side of $\Delta BPQ$ is $\frac{3}{4}$ of the corresponding sides of $\Delta ABC$. Write the steps of construction.