#"Incircle radius " r = A_t / s#
#A(5,2), B(1,3), C(7,4)#
#a = sqrt((7-1)^2 + (4-3)^2) = sqrt37#
#b = sqrt((7-5)^2 + (4-2)^2) = sqrt8#
#c = sqrt((5-1)^2 + ( 2-3)^2) = sqrt17#
#"Semi-perimeter " s = (a + b + c) / 2 = (sqrt37 + sqrt8 + sqrt17) / 2 = 6.52#
#"A_t = sqrt(s (s-a) s-b) (s-c))#
#A_t = sqrt(6.52 (6.52-sqrt37) (6.52 - sqrt8) (6.52 - sqrt17)) =5.0224#
#color(blue)("Radius of incircle " r = A_t / s = 5.0224 / 6.52 = 0.77 " units"#