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 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:

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 parallelogram $ABCD$ in which $BC = 5 \, cm$,$AB = 3 \, cm$ and $\angle ABC = 60^{\circ}$. Divide it into triangles $BCD$ and $ABD$ by the diagonal $BD$. Construct the triangle $BD'C'$ similar to $\triangle BDC$ with a scale factor of $\frac{4}{3}$. Draw the line segment $D'A'$ parallel to $DA$,where $A'$ lies on the extended side $BA$. Is $A'BCD'$ a parallelogram?

State whether the following statement is True or False and provide a reason for your answer:
$A$ pair of tangents can be constructed to a circle inclined at an angle of $170^{\circ}$.

Draw $\overline{AB}$ such that $AB = 10 \, cm$. Draw $\odot(A, 3)$ and $\odot(B, 4)$. Construct tangents to each circle through the centre of the other circle.