Here is the solution I came up with:

#macro LineIntersect(p1, d1, p2, d2)
 #local pSep = p2-p1;
 #local pdCross = vcross(d1,d2);
 #local pdLen = vlength(pdCross);
 #local lDist = vdot(pSep,pdCross);
 #local dist = vdot(vcross(pSep,d2),pdCross)/(pdLen*pdLen);
 #local pnt = p1+d1*dist;
 pnt
#end

#macro icRad(p1, p2, p3) // Inscribed circle radius
 #local ln1 = vlength(p2-p1);
 #local ln2 = vlength(p3-p1);
 #local ln3 = vlength(p3-p2);
 #local hPer = (ln1+ln2+ln3)*0.5;
 #local area = sqrt(hPer*(hPer-ln1)*(hPer-ln2)*(hPer-ln3));
 #declare rad = area/hPer;
 rad
#end

#macro icCen(p1, p2, p3) // Inscribed circle center
 #local dr1 = vnormalize(p3-p2);
 #local dr2 = vnormalize(p3-p1);
 #local dr3 = vnormalize(p2-p1);
 #local drb1 = vnormalize(-dr2-dr3); // Bisects angle through p1
 #local drb2 = vnormalize(dr3-dr1); // Bisects angle through p2
 #declare cen = LineIntersect(p1, drb1, p2, drb2);
 cen
#end

#macro ccRad(p1, p2, p3) // Circumscribed circle radius
 #local ln1 = vlength(p2-p1);
 #local ln2 = vlength(p3-p1);
 #local ln3 = vlength(p3-p2);
 #local hPer = (ln1+ln2+ln3)*0.5;
 #local area = sqrt(hPer*(hPer-ln1)*(hPer-ln2)*(hPer-ln3));
 #declare rad = ln1*ln2*ln3*0.25/area;
 rad
#end

#macro ccCen(p1, p2, p3) // Circumscribed circle center
 #local pNrm = vnormalize(vcross(p2-p1,p3-p1)); // Unit triangle plane
normal
 #local mp1 = (p2+p3)*.5; // Midpoint of line opposite p1
 #local mp2 = (p1+p3)*.5; // Midpoint of line opposite p2
 #local dr1 = vnormalize(vcross(p3-p2,pNrm));  // Perpincular to line opp.
p1
 #local dr2 = vnormalize(vcross(p3-p1,pNrm));  // Perpincular to line opp.
p2
 #declare cen = LineIntersect(mp1, dr1, mp2, dr2);
 cen
#end

My approach was simply set up the appropriate lines (angle bisectors for
incenter, perpendicular bisectors for circumcenter) and calculate the
intersection.  I found the solutions at MathWorld
(http://mathworld.wolfram.com/).  This approach is highly extensible and can
be used to calculate many triangle centers.

If anyone has a simpler solution that works in three dimensions (sorry,
Sputnik, your formula is for two), let me know.

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