Circles,
Circle inside a Triangle,
Circumcircle of a Triangle 

Circle (M,r) around the axis:

A circle with the center M with the radius R perpendicular to the axis N we get with a macro from "analytical_g.inc" :

Circle line:

object{ Circle_Line ( M, R, Rl, N)
        pigment{ color Yellow }}

Circle area:

object{ Circle_Disc ( M, R, N)
        pigment{ color rgb<1,1,0,0.5>}}

Representation of a circle in 3d
Circle around M with radius r and axis N

Click here for a complete description
of this scene for POV-Ray:
".txt" file or ".pov" file

Circumcircle - a circle around a triangle

A Circle around a triangle P₁P₂P₃ we can get by a macro from quot;analytical_g.inc" :

circle line:

object{ Circle_Line_out( P1, P2, P3, Rl)
        pigment{ color Yellow }}

circle area:

object{ Circle_Disc_out( P1, P2, P3 )
        pigment{ color rgb<1,1,0,0.5>}}

circumcircle center:

object{ Triangle_M_out( P1, P2, P3 )
        pigment{ color rgb<0,1,0,0.5> }}

circumcircle radius:

Triangle_R_out(  P1, P2, P3 ) 

Circumcircle of a triangle

Click here for a complete description
of this scene for POV-Ray:
".txt" file or ".pov" file

Incircle - a circle inside of a triangle

A circle inside of a triangle P₁P₂P₃ with a macro from "analytical_g.inc" :

circle linie:

object{ Circle_Line_in ( P1, P2, P3, Rl)
        pigment{ color Yellow }}

circle area:

object{ Circle_Disc_in ( P1, P2, P3 )
        pigment{ color Green transmit 0.5}}

Incircle center:

object{ Triangle_M_in ( P1, P2, P3 )
        pigment{ color Yellow transmit 0.5}}

Incircle radius:

Triangle_R_in (  P1, P2, P3 ) 

A circle inside of a triangle

Click here for a complete description
of this scene for POV-Ray:
".txt" file or ".pov" file