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 s−x4=s−y3=s−z2and area of in circle  of the triangle XYZ is  8π3, then

Given s−x4=s−y3=s−z2=ks-x=4ks-y=3ks-z=2k3s-2s=9ks=9kTherefore, x=5,y=6,z=7, S=9, Area =ss-as-bs-c=66r=∆S =263xyz=4R∆R=210246 =35624   r=4Rsinx2siny2sinz2 ⇒sinx2siny2sinz2=r4R=435sin2x+y2=1-cosx+y2 =1+cosz2 =121+x2+y2-z22xy =35