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.

Construct a tangent to a circle of radius $4\, cm$ from a point which is at a distance of $6\, cm$ from its centre.

Draw $\Delta ABC$ with $AB = 5 \text{ cm}$,$BC = 6 \text{ cm}$,and $m\angle B = 90^{\circ}$. Then,construct $\Delta BPQ$ similar to $\Delta ABC$ such that its sides are $\frac{3}{2}$ times the corresponding sides of $\Delta ABC$. Write the steps of construction.

Draw $\overline{PQ}$ of length $8.5 \text{ cm}$ and obtain point $X$ on $\overline{PQ}$ such that $PX : XQ = 4 : 7$. Write the steps of construction.

Draw a line segment $\overline{PQ}$ of length $8.2 \, cm$ and divide it in the ratio $3:7$ from point $P$. Write the steps of construction.

Write True or False and give reasons for your answer.
To construct a triangle similar to a given $\triangle ABC$ with its sides $\frac{7}{3}$ of the corresponding sides of $\triangle ABC$,draw a ray $BX$ making an acute angle with $BC$ and $X$ lies on the opposite side of $A$ with respect to $BC$. The points $B_{1}, B_{2}, \dots, B_{7}$ are located at equal distances on $BX$,$B_{3}$ is joined to $C$ and then a line segment $B_{6}C'$ is drawn parallel to $B_{3}C$ where $C'$ lies on $BC$ produced. Finally,line segment $A'C'$ is drawn parallel to $AC$.