X₁₉₇₃

TRILINEAR PRODUCT OF PU(39)

X₁₉₇₃ = barycentric product of PU(18)

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

X₁₉₇₃ (TRILINEAR PRODUCT OF PU(39)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 19}, {25, 41}

• Related Centers: X₃₀₄ (ISOTOMIC CONJUGATE OF X₁₉), X₁ (INCENTER), X₁₉ (CLAWSON POINT), X₂₅ (HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES), X₄₁ (-CEVA CONJUGATE OF X₃₁)

Trilinears: \(a^{3}\cos B \cos C : :\)

Search Value (6, 9, 13): \(-0.225154462927\)

▸ Alternate Coordinates1 form

• Trilinears: \(\tan A \sin^{2} A : :\)

▸ Incident Central Lines12 lines

{1, 19}, {6, 1245}, {25, 41}, {32, 1395}, {34, 1438}, {47, 163}, {112, 741}, {255, 1755}, {278, 1429}, {604, 608}, {1148, 1283}, {1842, 1886}

▸ Functional Relations12 relations

• X₁₉₇₃ = isogonal conjugate of X₃₀₄

• X₁₉₇₃ = complement of anticomplementary conjugate of X₂₁₂₁₆

• X₁₉₇₃ = X_i-Ceva conjugate of X_j for these (i,j): (19, 31), (608, 1395), (1474, 25)

• X₁₉₇₃ = X_i-cross conjuguate of X_j for these (i,j): (4, 683), (682, 3), (1196, 2), (1368, 305)

• X₁₉₇₃ = crosspoint of X_i and X_j for these (i,j): (19, 1096), (25, 608)

• X₁₉₇₃ = crosssum of X_i and X_j for these (i,j): (63, 326), (69, 345), (312, 322), (525, 1565)

• X₁₉₇₃ = barycentric product of PU(18)

• X₁₉₇₃ = trilinear product of intersections of circumcircle and 2nd Lemoine circle

• X₁₉₇₃ = pole wrt polar circle of trilinear polar of X₅₆₁

• X₁₉₇₃ = X₄₈-isoconjugate (polar conjugate) of X₅₆₁

• X₁₉₇₃ = X₇₅-isoconjugate of X₆₃

• X₁₉₇₃ = X₉₂-isoconjugate of X₃₂₆