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 :

Let $x=\frac{\sin ^2 A+\sin A+1}{\sin A}$ where 0 < A ≤ $\frac{\pi}{2}$

What is the minimum value of x ?

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

Let $x=\frac{\sin ^2 A+\sin A+1}{\sin A}$ where 0 < A ≤ $\frac{\pi}{2}$

At what value of A does x attain the minimum value ?

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 ?