Consider the following for the next two (02) items that follow :

In the triangle ABC, 

a² + b² + c² = ac + √3 bc

What is the nature of the triangle ? 

Consider the following for the next two (02) items that follow :

In the triangle ABC, 

a² + b² + c² = ac + √3 bc

If c = 8, what is the area of the triangle ?

Consider the following for the next two (02) items that follow :

In a triangle POR, P is the largest angle and cosP = $\frac{1}{3}$. Further the in-circle of the triangle touches the sides PQ, QR and RP at N, L and M respectively such that the lengths PN, QL and RM are n, n + 2, n + 4 respectively where n is an integer. 

What is the value of n ? 

Consider the following for the next two (02) items that follow :

In a triangle POR, P is the largest angle and cosP = $\frac{1}{3}$. Further the in-circle of the triangle touches the sides PQ, QR and RP at N, L and M respectively such that the lengths PN, QL and RM are n, n + 2, n + 4 respectively where n is an integer. 

What is the length of the smallest side ?