A(4, 5), B(1 3), C(3, 3)A(4,5),B(13),C(3,3)
c = sqrt((4-1)^2 + (5-3)^2) ~~ sqrt 13c=√(4−1)2+(5−3)2≈√13
a= sqrt ((1-3)^2 + (3-3)^2) ~~ 2a=√(1−3)2+(3−3)2≈2
b = sqrt((3-4)^2 + (3-5)^2) ~~ sqrt 5b=√(3−4)2+(3−5)2≈√5
Semi perimeter s = (a + b + c)/2 s=a+b+c2
s = (sqrt 13 + 2 + sqrt 5 ) / 2 = 3.9208s=√13+2+√52=3.9208
Area of triangle A_t = sqrt(s (s-a) (s-b) (s-c)), " using Heron's formula"At=√s(s−a)(s−b)(s−c), using Heron's formula
A_t = sqrt(3.9208 (3.9208- sqrt 13) (3.9208- 2) (3.9208-sqrt 5)) ~~ 2At=√3.9208(3.9208−√13)(3.9208−2)(3.9208−√5)≈2
color(indigo)("Radius of in-circle "= r = A_t / s = 2 / 3.9208 ~~ 0.5101Radius of in-circle =r=Ats=23.9208≈0.5101
