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:

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 construct a triangle similar to a given $\triangle ABC$ with its sides $\frac{3}{7}$ of the corresponding sides of $\triangle ABC$,first draw a ray $BX$ such that $\angle CBX$ is an acute angle and $X$ lies on the opposite side of $A$ with respect to $BC$. Then locate points $B_{1}, B_{2}, B_{3}, \dots$ on $BX$ at equal distances and the next step is to join

Draw a circle with the help of a round bowl turned upside-down. Take a point $P$ in the exterior of the circle and draw tangents to the circle from that point. Write the steps of construction.

Draw a triangle $ABC$ in which $AB = 4 \, cm$,$BC = 6 \, cm$,and $AC = 9 \, cm$. Construct a triangle similar to $\triangle ABC$ with a scale factor of $\frac{3}{2}$. Justify the construction. Are the two triangles congruent? Note that all three angles of the two triangles are equal,but the sides are not.

Draw $\overline{AB}$ of length $10 \,cm$ and divide it in the ratio $3:8$ from $A$. Write the steps of construction.