Here is a file that I wrote that does it a little bit differently.  It
calculates the three vectors for the sides of the triangle.  Then it
picks a point inside the triangle by multiplyng one edge vector by a
random number between 0 and 1, finding the vector to the opposite
corner, and then multiplying that by a random number between 0 and 1. 
This always yields a point inside the triangle.  Then it calculates the
perpendicular distances to the three edges and uses the smallest
distance for the radius.

camera{
     location <4,4,-10>
     look_at <0,0,0>
     }

light_source{
     <10,7,-20>
     color rgb <1,1,1>
     }

#declare P1 = <-3,-3,0>   \\ put your three points here
#declare P2 = <0,4,0>
#declare P3 = <3,0,0>

#declare A=seed(3)

#declare vec1 = P2-P1
#declare vec2 = P3-P2
#declare vec3 = P1-P3

#declare counter = 0
#while (counter < 300)
     #declare some_center = P1 + rand(A)*((vec2 * rand(A))+vec1)
     #declare dist_vec1 = vlength(
vcross(vec1,(some_center-P2)))/vlength(vec1)
     #declare dist_vec2 = vlength(
vcross(vec2,(some_center-P3)))/vlength(vec2)
     #declare dist_vec3 = vlength(
vcross(vec3,(some_center-P1)))/vlength(vec3)
     
     sphere{
          some_center, min(dist_vec1, min(dist_vec2,dist_vec3) )
                   \\ draw a circle that touches the edge of the
triangle
          pigment{ color rgb <0,1,1>}
     }
     
     #declare counter = counter + 1
#end

triangle{
     P1, P2, P3
     pigment { color rgb <1,1,1> }
     }

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