To divide a line segment $AB$ in the ratio $5:7,$ first a ray $AX$ is drawn so that $\angle BAX$ is an acute angle and then at equal distances points are marked on the ray $AX$ such that the minimum number of these points is

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.

Draw a line segment of length $7 \, cm$. Find a point $P$ on it which divides it in the ratio $3: 5$.

Draw $\Delta ABC$ with $AB = 6 \, cm$,$BC = 8 \, cm$,and $m\angle B = 60^\circ$. Then,construct $\Delta BXY$ similar to $\Delta ABC$ whose sides have lengths $\frac{4}{5}$ times the lengths of the corresponding sides of $\Delta ABC$. Write the steps of construction.

Draw $\odot( P , 3 \, cm )$ and a diameter $\overline{ AB }$ in it. Take points $X$ and $Y$ such that $X - A - B$ and $A - B - Y$ where $PX = PY = 7 \, cm$. From $X$ and $Y$,draw tangents to $\odot( P , 3 \, cm )$. 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.