X₁₉₃₅

CROSSSUM OF PU(15)

X₁₉₃₅ = X₂₉₆-Ceva conjugate of X₁₉₃₆

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

X₁₉₃₅ (CROSSSUM OF PU(15)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 90}, {21, 73}

• Related Centers: X₂₉₆ (ISOGONAL CONJUGATE OF X₂₄₃), X₁₉₃₆ (CROSSDIFFERENCE OF PU(15)), X₁ (INCENTER), X₉₀ (-CROSS CONJUGATE OF X₁), X₂₁ (SCHIFFLER POINT), X₇₃ (CROSSPOINT OF INCENTER AND CIRCUMCENTER)

Trilinears: \(\cos^{2} A + \cos B \cos C : :\)

Search Value (6, 9, 13): \(1.269759043475\)

▸ Alternate Coordinates1 form

• Trilinears: \((a^{4} - a^{2} (b^{2} + b c + c^{2}) + b c (b + c)^{2})/(a - b - c) : :\)

▸ Incident Central Lines34 lines

{1, 90}, {2, 603}, {3, 1745}, {4, 255}, {7, 1451}, {9, 478}, {10, 109}, {12, 171}, {20, 212}, {21, 73}, {31, 388}, {34, 63}, {40, 1777}, {47, 1478}, {56, 87}, {57, 1724}, {58, 226}, {65, 1046}, {84, 1040}, {221, 958}, {222, 405}, {225, 283}, {415, 1098}, {497, 1496}, {748, 1106}, {774, 1776}, {896, 1254}, {940, 1806}, {960, 1455}, {978, 1470}, {1056, 1497}, {1400, 1778}, {1448, 1708}, {1761, 1880}

▸ Functional Relations6 relations

• X₁₉₃₅ = X₂₉₆-Ceva conjugate of X₁₉₃₆

• X₁₉₃₅ = cevapoint of X₁₀₄₆ and X₁₇₄₅

• X₁₉₃₅ = crosspoint of PU(16)

• X₁₉₃₅ = intersection of tangents at PU(16) to conic {A, B, C,PU(16)}

• X₁₉₃₅ = perspector of ABC and the side-triangle of the 1st and 2nd bicentrics of the orthic triangle

• X₁₉₃₅ = {X₃₄,X₆₃}-harmonic conjugate of X₃₇₅₉₁