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In a \( \triangle X Y Z \), let \( x, y, z \) be the lengths of sides opposite to the angles \( X, Y, Z \) respectively and \( 2 s=x+y+z \).
P
If \( \frac{s-x}{4}=\frac{s-y}{3}=\frac{s-z}{2} \) and area of incircle of the
W
\( \triangle X Y Z \) is \( \frac{8 \pi}{3} \), then
(2016 Adv.)
(a) area of the \( \triangle X Y Z \) is \( 6 \sqrt{6} \)
(b) the radius of circumcircle of the \( \triangle X Y Z \) is \( \frac{35}{6} \sqrt{6} \)
(c) \( \sin \frac{X}{2} \sin \frac{Y}{2} \sin \frac{Z}{2}=\frac{4}{35} \)
(d) \( \sin ^{2}\left(\frac{X+Y}{2}\right)=\frac{3}{5} \)
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