The area #S# can be computed with Eron's formula:
#S=sqrt(p(p-a)(p-b)*(p-c))#
where #p=(a+b+c)/2#.
Substituting in the formula:
#r=(sqrt(p(p-a)(p-b)*(p-c)))/(p)#
Start calculating the lengths of the sides:
#a=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#
#b=sqrt((x_3-x_2)^2+(y_3-y_2)^2)#
#c=sqrt((x_1-x_3)^2+(y_1-y_3)^2)#
#a = sqrt((9-4)^2+(2-7)^2) = sqrt(25+25) = 5sqrt(2)#
#b= sqrt((5-4)^2+(8-7)^2) =sqrt(1+1) =sqrt(2)#
#c= sqrt((9-5)^2+(8-2)^2) =sqrt(16+36) =2sqrt(13)#
#p=(5sqrt(2)+sqrt(2)+2sqrt(13))/2 = 3sqrt(2)+sqrt(13)#
#r=sqrt((3sqrt(2)+sqrt(13))(3sqrt(2)+sqrt(13)-5sqrt(2))(3sqrt(2)+sqrt(13)-sqrt(2))(3sqrt(2)+sqrt(13)-2sqrt(13)))/(3sqrt(2)+sqrt(13))=sqrt((3sqrt(2)+sqrt(13))(sqrt(13)-2sqrt(2))(2sqrt(2)+sqrt(13))(3sqrt(2)-sqrt(13)))/(3sqrt(2)+sqrt(13))#
and I leave the rest of the calculation :D