已知D.E.F分别是锐角三角形ABC的三边BC,CA,AB上的点,

x/(x+6)=PD/AD=Spbc/Sabc,
y/(y+6)=PE/BE=Spac/Sabc,
z/(z+6)=PF/CF=Spab/Sabc,
所以
x/(x+6)+y/(y+6)+z/(z+6)=1
6/(x+6)+6/(y+6)+6/(z+6)=2
.6(xy+yz+zx+12(x+y+z)+108)=2(xyz+6(xy+yz+xz)+36(x+y+z)+216)
2xyz=648-432-6(xy+yz+xz)
xyz=324-216-3*28=108-84=24.