The area SS can be computed with Eron's formula:
S=sqrt(p(p-a)(p-b)*(p-c))S=√p(p−a)(p−b)⋅(p−c)
where p=(a+b+c)/2p=a+b+c2.
Substituting in the formula:
r=(sqrt(p(p-a)(p-b)*(p-c)))/(p)r=√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)a=√(x2−x1)2+(y2−y1)2
b=sqrt((x_3-x_2)^2+(y_3-y_2)^2)b=√(x3−x2)2+(y3−y2)2
c=sqrt((x_1-x_3)^2+(y_1-y_3)^2)c=√(x1−x3)2+(y1−y3)2
a = sqrt((9-4)^2+(2-7)^2) = sqrt(25+25) = 5sqrt(2)a=√(9−4)2+(2−7)2=√25+25=5√2
b= sqrt((5-4)^2+(8-7)^2) =sqrt(1+1) =sqrt(2)b=√(5−4)2+(8−7)2=√1+1=√2
c= sqrt((9-5)^2+(8-2)^2) =sqrt(16+36) =2sqrt(13)c=√(9−5)2+(8−2)2=√16+36=2√13
p=(5sqrt(2)+sqrt(2)+2sqrt(13))/2 = 3sqrt(2)+sqrt(13)p=5√2+√2+2√132=3√2+√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
