X₅₅₅

(X₁,X₁₅₈)-ANSWER TO QUESTION A

X₅₅₅ = isotomic conjugate of X₆₇₃₁

5, 6, 7 3, 4, 5 Kepler Kimberling

X₅₅₅ ((X₁,X₁₅₈)-ANSWER TO QUESTION A) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {7, 177}, {234, 1088}

• Related Centers: X₇ (GERGONNE POINT), X₁₇₇ (1st MID-ARC POINT), X₂₃₄ (-CEVA CONJUGATE OF X₁₇₇), X₁₀₈₈ (TRILINEAR SQUARE OF X₇)

Trilinears: \(\sec^{3}(A/2) : \sec^{3}(B/2) : \sec^{3}(C/2)\)

Barycentrics: \(\sin A \sec^{3}(A/2) : \sin B \sec^{3}(B/2) : \sin C \sec^{3}(C/2)\)

Search Value (6, 9, 13): \(0.437625772792\)

▸ Alternate Coordinates2 forms

• Trilinears: \(|AJa| : :\), where J_a = A-mixtilinear excenter

• Barycentrics: \((-a + b - c) \cdot (a + b - c) \sqrt{b (a + b - c) c (a - b + c)} : :\)

▸ Incident Central Lines6 lines

{7, 177}, {85, 2090}, {188, 4146}, {234, 1088}, {279, 16015}, {10481, 10489}

▸ Functional Relations9 relations

• X₅₅₅ = isotomic conjugate of X₆₇₃₁

• X₅₅₅ = isotomic conjugate of the isogonal conjugate of X₇₃₇₀

• X₅₅₅ = X_i-cross conjugate of X_j for these (i,j): {174, 4146}, {234, 7}

• X₅₅₅ = cevapoint of X_i and X_j for these (i,j): {7, 18886}, {174, 7371}, {514, 10491}

• X₅₅₅ = barycentric product X_i*X_j for these {i,j}: {7, 4146}, {75, 7371}, {76, 7370}, {85, 174}, {188, 1088}, {266, 6063}, {279, 556}, {479, 7027}, {4569, 6728}, {6729, 46406}, {6730, 36838}, {6731, 23062}

• X₅₅₅ = X_i-Dao conjugate of X_j for these (i,j): {2, 6731}, {9, 6726}, {9, 15495}, {174, 17113}, {188, 3160}, {200, 236}, {223, 259}, {556, 40593}, {845, 7371}, {1086, 6730}, {1214, 6725}, {3082, 5431}, {6376, 7027}, {6728, 40615}, {6729, 40617}

• X₅₅₅ = X_i-isoconjugate of X_j for these (i,j): {6, 6726}, {31, 6731}, {32, 7027}, {41, 188}, {55, 259}, {174, 1253}, {220, 266}, {480, 7370}, {556, 2175}, {657, 6733}, {692, 6730}, {1334, 6727}, {2194, 6725}, {2332, 7591}, {3939, 6729}, {4146, 14827}, {6602, 7371}

• X₅₅₅ = barycentric quotient X_i/X_j for these {i,j}: {1, 6726}, {2, 6731}, {7, 188}, {57, 259}, {75, 7027}, {85, 556}, {174, 9}, {188, 200}, {226, 6725}, {234, 16016}, {259, 220}, {266, 55}, {269, 266}, {279, 174}, {479, 7371}, {508, 4182}, {509, 4166}, {514, 6730}, {556, 346}, {738, 7370}, {934, 6733}, {1014, 6727}, {1088, 4146}, {1439, 7591}, {2091, 15997}, {3668, 6724}, {3669, 6729}, {3676, 6728}, {4146, 8}, {5451, 34912}, {6724, 210}, {6725, 4515}, {6726, 480}, {6727, 2328}, {6728, 3900}, {6729, 657}, {6730, 4130}, {6731, 728}, {6733, 3939}, {7027, 5423}, {7370, 6}, {7371, 1}, {7591, 2318}, {10490, 16012}, {14596, 7707}, {18886, 236}, {21456, 7028}

• X₅₅₅ = {X_i,X_j}-harmonic conjugate of X_k for these (i,j,k): {10489, 10491, 10481}, {18886, 21456, 279}