In each of the following, give also the justification of the construction:
Draw a line segment $AB$ of length 8 cm. Taking $A$ as centre, draw a circle of radius 4 cm and taking $B$ as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.

In each of the following, give also the justification of the construction:
Let ABC be a right triangle in which $AB = 6$ cm, $BC = 8$ cm and $\angle B = 90^{\circ}$. $BD$ is the perpendicular from $B$ on $AC$. The circle through $B$, $C$, $D$ is drawn. Construct the tangents from $A$ to this circle.

In each of the following, give also the justification of the construction:
Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle.

In each of the following, give also the justification of the construction:
Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.

In each of the following, give also the justification of the construction:
Draw a circle of radius 3 cm. Take two points $P$ and $Q$ on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points $P$ and $Q$.

In each of the following, give also the justification of the construction:
Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of $60^{\circ}$.

In each of the following, give also the justification of the construction:
Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.