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

The perimeter of a triangle ABC is 6 times the AM of sine of angles of the triangle.

Further BC = √3 and CA = 1

Consider the following statements :

1. ABC is right angled triangle

2. The angles of the triangle are in AP

Which of the statements given above is/are correct ? 

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

In the triangle ABC, 

a² + b² + c² = ac + √3 bc

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

In the triangle ABC, 

a² + b² + c² = ac + √3 bc

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.