X(73098) = 1ST HATZIPOLAKIS-MOSES-MALFATTI POINT
Barycentrics Sin[A]*(3 + Tan[B/4]^2*Tan[C/4]^2 + Tan[A/4]*(-2 + 2*Tan[C/4] + Tan[B/4]*(2 + 2*Tan[C/4]) + Tan[A/4]*(4 + Tan[B/4]*(2 - Tan[B/4] - 2*Tan[C/4]) + (2 - Tan[C/4])*Tan[C/4]))) : :X(73098) = (3 + c0 - s0)*X[1] + (1 - c0 + s0)*X[167], where s0 = Sin[A/2] + Sin[B/2] + Sin[C/2] and c0 = Cos[A/2] + Cos[B/2] + Cos[C/2]
Antreas Hatzipolakis and Peter Moses, euclid 10392.
X(73098) lies on these lines: {1, 167}, {40, 483}, {164, 1489}, {1127, 1129}, {8225, 12523}
X(73098) = reflection of X(73099) in X(73100)
X(73098) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 8351, 73099}, {1127, 1129, 21465}
X(73099) = 2ND HATZIPOLAKIS-MOSES-MALFATTI POINT
Barycentrics Sin[A]*(3 + Cot[B/4]^2*Cot[C/4]^2 + Cot[A/4]*(-2 + 2*Cot[C/4] + Cot[B/4]*(2 + 2*Cot[C/4]) + Cot[A/4]*(4 + Cot[B/4]*(2 - Cot[B/4] - 2*Cot[C/4]) + (2 - Cot[C/4])*Cot[C/4]))) : :X(73099) = (3 - c0 - s0)*X[1] + (1 + c0 + s0)*X[167], where s0 = Sin[A/2] + Sin[B/2] + Sin[C/2] and c0 = Cos[A/2] + Cos[B/2] + Cos[C/2]
Antreas Hatzipolakis and Peter Moses, euclid 10392.
X(73099) lies on these lines: {1, 167}, {40, 3082}, {164, 41885}, {10230, 10232}, {12523, 31546}
X(73099) = reflection of X(73098) in X(73100)
X(73099) = {X(1),X(8351)}-harmonic conjugate of X(73098)
X(73100) = 3RD HATZIPOLAKIS-MOSES-MALFATTI POINT
Barycentrics Sin[A]*(4*(1 - Tan[A/4]*Tan[B/4] - Tan[A/4]*Tan[C/4] - Tan[B/4]*Tan[C/4])*(1 + Tan[A/4]*Tan[B/4]*Tan[C/4]) + (-1 + Tan[A/4]*Tan[B/4]*Tan[C/4])*(3 - 2*Tan[A/4]*(1 - Tan[A/4] - Tan[B/4] - Tan[C/4])*(1 - Tan[A/4]*Tan[B/4] - Tan[A/4]*Tan[C/4] - Tan[B/4]*Tan[C/4]) + (Tan[A/4]*Tan[B/4] + Tan[A/4]*Tan[C/4] + Tan[B/4]*Tan[C/4])^2 + 2*Tan[A/4]^2*(1 + Tan[A/4]*Tan[B/4] + Tan[A/4]*Tan[C/4] + Tan[B/4]*Tan[C/4]))) : :X(73100) = 3 X[3576] - X[9836], X[12884] + 3 X[55175]
X(73100) = (3 - s0)*X[1] + (1 + s0)*X[167], where s0 = Sin[A/2] + Sin[B/2] + Sin[C/2]
Antreas Hatzipolakis and Peter Moses, euclid 10392.
X(73100) lies on these lines: {1, 167}, {3, 18258}, {21, 8110}, {40, 168}, {100, 7597}, {164, 7028}, {1001, 12523}, {3576, 9836}, {3913, 12518}, {6261, 31791}, {12884, 55175}, {20183, 60598}, {31790, 64733}
X(73100) = midpoint of X(i) and X(j) for these {i,j}: {40, 9837}, {73098, 73099}
X(73100) = reflection of X(52797) in X(3)
