A) Construct a triangle ABC with AB = 8cm, AC = 7cm, BC = 6cm.

Here are the steps to solve the problem:

a) Construct a triangle ABC with AB = 8cm, AC = 7cm, BC = 6cm.

Construction Steps:

1. Draw a straight line segment and mark a point A on it.
2. From point A, measure and mark point B such that the length of segment AB is $8 \text{ cm}$.
3. Place the compass at point A and open it to a radius of $7 \text{ cm}$. Draw an arc above the line segment AB.
4. Place the compass at point B and open it to a radius of $6 \text{ cm}$. Draw another arc above the line segment AB, ensuring it intersects the first arc.
5. Mark the point of intersection of the two arcs as C.
6. Draw straight lines connecting A to C and B to C.
7. Triangle ABC is now constructed with sides $AB = 8 \text{ cm}$, $AC = 7 \text{ cm}$, and $BC = 6 \text{ cm}$.

b) Give a special name to this triangle.

Since all three sides of the triangle have different lengths ($8 \text{ cm}$, $7 \text{ cm}$, $6 \text{ cm}$), the triangle is a:

$$\boxed{\text{Scalene triangle}}$$

c) Bisect any two sides of this triangle and mark X the point of intersection of the bisections.

Bisection Steps (using sides AB and AC as an example):

1. Bisect side AB:
   • Place the compass at point A and open it to a radius greater than half the length of AB. Draw arcs above and below the line segment AB.
   • Without changing the compass radius, place the compass at point B and draw arcs above and below AB, intersecting the first set of arcs.
   • Draw a straight line connecting the two points where the arcs intersect. This line is the perpendicular bisector of AB.
2. Bisect side AC:
   • Place the compass at point A and open it to a radius greater than half the length of AC. Draw arcs on both sides of the line segment AC.
   • Without changing the compass radius, place the compass at point C and draw arcs on both sides of AC, intersecting the previous set of arcs.
   • Draw a straight line connecting the two points where these arcs intersect. This line is the perpendicular bisector of AC.
3. Mark the intersection:
   • The point where the perpendicular bisector of AB and the perpendicular bisector of AC intersect is marked as X. This point X is the circumcenter of the triangle.