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

Divide a line segment into three parts in the ratio $2: 3: 4$ in the same order.

Draw $\odot(O, 4\, cm)$ and a diameter $\overline{PQ}$ in it. Take points $A$ and $B$ such that $A-P-Q$ and $P-Q-B$. From $A$ and $B$,draw tangents to $\odot(O, 4\, cm)$. Write the steps of construction.

Write True or False and give reasons for your answer.
$A$ pair of tangents can be constructed from a point $P$ to a circle of radius $3.5 \, cm$ situated at a distance of $3 \, cm$ from the centre.

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 $\frac{5}{3}$.