Construct an incircle of an equilateral triangle with side $4.6 \mathrm{cm}$.

Construct a circumcircle of $△ABC$, where $AB=8 cm, BC=5 cm$and $\angle ABC = 60°$degree. Write the steps of construction.

Consider the following statements:

1. The point of intersection of the perpendicular bisectors of the sides of a triangle may lie outside the triangle.

2. The point of intersection of the perpendiculars drawn from the vertices to the opposite sides of a triangle may lie on two sides.

Which of the above statements is/are correct?

Consider the following statements:

$1.$The orthocentre of a triangle always lies inside the triangle.

$2.$The centroid of a triangle always lies inside the triangle.

$3.$The orthocentre of a right-angled triangle lies on the triangle.

$4.$The centroid of a right-angled triangle lies on the triangle.

Which of the above statements are correct?

Construct two circles of radii $4 \mathrm{cm}$ and $2 \mathrm{cm}$ and the distance between their centres is $7 \mathrm{cm}$. Construct a direct common tangent of the circles. (only traces of construction are required).