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JEE Advanced 2016 Paper 1 Mathematics Question 45

In a triangle XYZ, let x, y, z be the lengths of sides opposite to the angles X, Y, Z respectively, and \(2s = x + y + z\). If \(\displaystyle\frac{s-x}{4} = \frac{s-y}{3} = \frac{s-z}{2}\) and area of incircle of the triangle XYZ is \(\displaystyle\frac{8\pi}{3}\), then