A triangle \(A B C\) have sides \(x+y=11 ; 2 x+3 y=29\) and \(x+2y=16\) such that a point \(P\left(\frac{11}{2}, \alpha\…

A triangle \(A B C\) have sides \(x+y=11 ; 2 x+3 y=29\) and \(x+2y=16\) such that a point \(P\left(\frac{11}{2}, \alpha\right)\) lies on or inside the triangle find the product of maximum and minimum value of " \(\alpha\) ".