incenter, 1
centroid, 1/a
circumcenter, a(b^2+c^2-a^2)
orthocenter, 1/(a(b^2+c^2-a^2))
nine point center, (a^2b^2+a^2c^2+2b^2c^2-b^4-c^4)/a
symmedian point, a
Gergonne point, 1/(a(b+c-a))
Nagel point, (b+c-a)/a
Mittenpunkt, b+c-a
Spieker center, (b+c)/a
Feuerbach point, ((-b + c)^2*(-a + b + c))/a
X12, (b + c)^2/(a(b+c-a))
1st isogonic center (Fermat point), (Sqrt[3](b^2+c^2-a^2)-4K)/(a(-a^2+b^2-b*c+c^2)*(-a^2+b^2+b*c+c^2))
2nd Isogonic center, (Sqrt[3](a^2-b^2-c^2)-4K)/(a(-a^2+b^2-b*c+c^2)*(-a^2+b^2+b*c+c^2))
1st Isodynamic point, a(Sqrt[3](b^2+c^2-a^2)+4*K)
2nd Isodynamic point, a(Sqrt[3](a^2-b^2-c^2)+4*K)
1st Napoleon point, ((-a^2+b^2+c^2-4Sqrt[3]K))/(a(a^4-2a^2b^2+b^4-2a^2c^2-b^2c^2+c^4))
2nd Napoleon point, ((a^2-b^2-c^2-4Sqrt[3]K))/(a(a^4-2a^2b^2+b^4-2a^2c^2-b^2c^2+c^4))
Crucial point, 1/(-a^2 + b^2 + c^2)
De Longchamps point, (-3*a^4 + 2*a^2*b^2 + b^4 + 2*a^2*c^2 - 2*b^2*c^2 + c^4)/a
Schiffler point, (b+c-a)/(b + c)
Exeter point, a(b^4+c^4-a^4)
far out point, a(b^4+c^4-a^4-b^2c^2)
X24, a(-a^4 + 2*a^2*b^2 - b^4 + 2*a^2*c^2 - c^4)/(a^2 - b^2 - c^2)
X25, a/(b^2+c^2-a^2)
Circumcenter of tangential triangle, a(-a^8+2a^6*b^2-2a^2*b^6+b^8+2a^6*c^2-2b^6*c^2+2b^4*c^4-2a^2*c^6-2b^2*c^6+c^8)
X27, 1/(a(b + c)*(-a^2 + b^2 + c^2))
X28, 1/((b + c)*(-a^2 + b^2 + c^2))
X29, (a - b - c)/(a(b + c)*(a^2 - b^2 - c^2))
X30, (2a+b+c)/a
2nd power point, a^2
3rd power point, a^3
X33, (-a + b + c)/(-a^2 + b^2 + c^2)
X34, 1/((-a^2 + b^2 + c^2)(b+c-a))
X35, a(-a^2 + b^2 + b*c + c^2)
X36, a(a^2 - b^2 + b*c - c^2)
X37, b+c
X38, b^2+c^2
Brocard midpoint, a(b^2+c^2)
X40, (a^3+a^2*b-a*b^2-b^3+a^2*c-2*a*b*c+b^2*c-a*c^2+b*c^2-c^3)
X41, a^2(b+c-a)
X42, a(b+c)
X43, c a+a b-b c
X44, b+c-2a
X45, 2b+2c-a
X46, a^3 + a^2*b - a*b^2 - b^3 + a^2*c + b^2*c - a*c^2 + b*c^2 - c^3
X47, a^2(a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + c^4)
X48, a^2(-a^2 + b^2 + c^2)
X49, a^3(a^2 - b^2 - c^2)(-a^4 + 2*a^2*b^2 - b^4 + 2*a^2*c^2 + b^2*c^2 - c^4)
X50, a^3*(a^2 - b^2 - b*c - c^2)*(a^2 - b^2 + b*c - c^2)
Centroid of orthic triangle, a(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)
Orthocenter of orthic triangle, a(a^2*b^2-b^4+a^2*c^2+2*b^2*c^2-c^4)*(a^4-2*a^2*b^2+b^4-2*a^2*c^2+c^4)
Symmedian point of orthic triangle, (a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)/(a(-a^2 + b^2 + c^2))
Nine point inv, a/(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)
Gergonne inv, a(b+c-a)
Nagel inv, a/(-a + b + c)
Mittenpunkt inv, 1/(b+c-a)
Spieker inv, a/(b+c)
Feuerbach inv, a/((-b + c)^2*(-a + b + c))
X12 inv, a(b+c-a)/(b+c)^2
1st Napoleon point inv, a(-a^2 + b^2 + c^2 + 4Sqrt[3]K)
2nd Napoleon point inv, a(a^2 - b^2 - c^2 + 4Sqrt[3]K)
Crucial point inv, b^2+c^2-a^2
De Longchamps point inv, a/(-3*a^4 + 2*a^2*b^2 + b^4 + 2*a^2*c^2 - 2*b^2*c^2 + c^4)
Schiffler point inv, (b + c)/(b+c-a)
Exeter point inv, 1/(a(b^4+c^4-a^4))
far out point inv, 1/(a(b^4+c^4-a^4-b^2c^2))
X24 inv, (a^2 - b^2 - c^2)/(a(-a^4 + 2*a^2*b^2 - b^4 + 2*a^2*c^2 - c^4))
X25 inv, (b^2+c^2-a^2)/a
Circumcenter of tangential triangle inv, 1/(a(-a^8+2a^6*b^2-2a^2*b^6+b^8+2a^6*c^2-2b^6*c^2+2b^4*c^4-2a^2*c^6-2b^2*c^6+c^8))
X27 inv, a(b + c)*(-a^2 + b^2 + c^2)
X28 inv, (b + c)*(-a^2 + b^2 + c^2)
X29 inv, (a(b + c)*(a^2 - b^2 - c^2))/(a - b - c)
X30 inv, a/(-2*a^4 + a^2*b^2 + b^4 + a^2*c^2 - 2*b^2*c^2 + c^4)
2nd power point inv, 1/a^2
3rd power point inv, 1/a^3
X33 inv, (-a^2 + b^2 + c^2)/(-a + b + c)
X34 inv, (-a^2 + b^2 + c^2)(b+c-a)
X35 inv, 1/(a(-a^2 + b^2 + b*c + c^2))
X36 inv, 1/(a(a^2 - b^2 + b*c - c^2))
X37 inv, 1/(b+c)
X38 inv, 1/(b^2+c^2)
Brocard midpoint inv, 1/(a(b^2+c^2))
X40 inv, 1/(a^3+a^2*b-a*b^2-b^3+a^2*c-2*a*b*c+b^2*c-a*c^2+b*c^2-c^3)
X41 inv, 1/(a^2(b+c-a))
X42 inv, 1/(a(b+c))
X43 inv, 1/(c a+a b-b c)
X44 inv, 1/(b+c-2a)
X45 inv, 1/(2b+2c-a)
X46 inv, 1/(a^3 + a^2*b - a*b^2 - b^3 + a^2*c + b^2*c - a*c^2 + b*c^2 - c^3)
X47 inv, 1/(a^2(a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + c^4))
X48 inv, 1/(a^2(-a^2 + b^2 + c^2))
X49 inv, 1/(a^3(a^2 - b^2 - c^2)(-a^4 + 2*a^2*b^2 - b^4 + 2*a^2*c^2 + b^2*c^2 - c^4))
X50 inv, 1/(a^3*(a^2 - b^2 - b*c - c^2)*(a^2 - b^2 + b*c - c^2))
Centroid of orthic triangle inv, 1/(a(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4))
Orthocenter of orthic triangle inv, 1/(a(a^2*b^2-b^4+a^2*c^2+2*b^2*c^2-c^4)*(a^4-2*a^2*b^2+b^4-2*a^2*c^2+c^4))
Symmedian point of orthic triangle inv, (a(-a^2 + b^2 + c^2))/(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)
Tarry point, 1/(a(-(a^2*b^2) + b^4 - a^2*c^2 + c^4))
Steiner point, ((-a + b)*(-a + c))/(a(b+c))
X100, (-a + b)*(-a + c)
X101, a*(-a + b)*(-a + c)
X102, 1/(a^2(b+c)-a b c)
X103, a/(b^2-c^2)
X104, (b-c)/a^2
X105, a/((b-a)(c-a))
X106, a^2(b+c)
X107, 1/(a^2(b+c))
X108, a/(b^2+c^2)
X109, a^2(b^2+c^2)
X110, 1/(a^2(b^2+c^2))
X111, (b^2+c^2)/a
X112, a(b+c-2a)
X113, 1/(a(b+c-2a))
X114, a/(b+c-2a)
X115, a^2(b+c-2a)
X116, 1/(a^2(b+c-2a))
X117, b+c-b c/a
r-power point, a^r
r2-power point, (b^r+c^r)/a
r3-power point, (b^r+c^r-a^r)/a
Z1, a^r(b+c)
Z2, a^r(b^2+c^2)
Z3, a^r(b+c-a)
Z4, a^r(b+c-2a)
Z5, a^r(b^2+c^2-a^2)
Z6, a^r(b^3+c^3)
Z7, a^r(b^2+c^2+b c)
Z8, a^r g[b,c]
r4-power point, (b^r+c^r+2a^r)/a
arbitrary center, f[a,g[b,c]]
areal center, f[a,b,c]/a

