In each of the following, give the justification of the construction also:
Draw a triangle ABC with side $BC = 7$ cm, $\angle B = 45^{\circ}$, $\angle A = 105^{\circ}$. Then, construct a triangle whose sides are $\frac{4}{3}$ times the corresponding sides of $\triangle ABC$.

In each of the following, give the justification of the construction also:
Draw a triangle ABC with side $BC = 6$ cm, $AB = 5$ cm and $\angle ABC = 60^{\circ}$. Then construct a triangle whose sides are $\frac{3}{4}$ of the corresponding sides of the triangle ABC.

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:
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 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:
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 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:
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 the justification of the construction also:
Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are $1\frac{1}{2}$ times the corresponding sides of the isosceles triangle.

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.

In each of the following, give the justification of the construction also:
Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are $\frac{2}{3}$ of the corresponding sides of the first triangle.

In each of the following, give the justification of the construction also:
Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are $\frac{7}{5}$ of the corresponding sides of the first triangle.

In each of the following, give the justification of the construction also:
Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are $\frac{5}{3}$ times the corresponding sides of the given triangle.

In each of the following, give the justification of the construction also:
Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts.