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 $\odot(P, 3\, cm)$ and take a point $R$ in its exterior such that $PR = 6\, cm$. Draw two tangents to $\odot(P, 3\, cm)$ from $R$. Write the steps of construction.

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 $^{\circ}$)

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.

Draw a circle of radius $5 \, cm$. From a point $8 \, cm$ away from the centre,construct two tangents to the circle. Measure their lengths.