To draw a pair of tangents to a circle which are inclined to each other at an angle of $60^{\circ},$ it is required to draw tangents at the endpoints of those two radii of the circle,the angle between which should be: (in $^{\circ}$)

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 being $\frac{8}{5}$ of the corresponding sides of $\triangle ABC$,a ray $BX$ is drawn such that $\angle CBX$ is an acute angle and $X$ is on the opposite side of $A$ with respect to $BC$. The minimum number of points to be located at equal distances on ray $BX$ is

Draw a triangle $ABC$ in which $BC = 6 \, cm$,$CA = 5 \, cm$,and $AB = 4 \, cm$. Construct a triangle similar to it with a scale factor of $\frac{5}{3}$.

Draw a circle $\odot(O, 4 \text{ cm})$ and take a point $X$ in its exterior at a distance of $7 \text{ cm}$ from $O$. Draw two tangents to the circle from point $X$. Write the steps of construction.

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.