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 $\frac{s-x}{4} = \frac{s-y}{3} = \frac{s-z}{2}$ and area of incircle of the triangle $XYZ$ is $\frac{8\pi}{3}$, then (A) area of the triangle $XYZ$ is $6\sqrt{6}$ (B) the radius of circumcircle of the triangle $XYZ$ is $\frac{35}{6}\sqrt{6}$ (C) $\sin\frac{X}{2}\sin\frac{Y}{2}\sin\frac{Z}{2} = \frac{4}{35}$ (D) $\sin^2\left(\frac{X+Y}{2}\right) = \frac{3}{5}$
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 $\frac{s-x}{4} = \frac{s-y}{3} = \frac{s-z}{2}$ and area of incircle of the triangle $XYZ$ is $\frac{8\pi}{3}$, then\\
(A) area of the triangle $XYZ$ is $6\sqrt{6}$\\
(B) the radius of circumcircle of the triangle $XYZ$ is $\frac{35}{6}\sqrt{6}$\\
(C) $\sin\frac{X}{2}\sin\frac{Y}{2}\sin\frac{Z}{2} = \frac{4}{35}$\\
(D) $\sin^2\left(\frac{X+Y}{2}\right) = \frac{3}{5}$