X₁₅₁₉

ORTHOJOIN OF X₉

X₁₅₁₉ = orthopole of PU(96)

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

X₁₅₁₉ (ORTHOJOIN OF X₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 4}, {119, 517}

• Related Centers: X₁ (INCENTER), X₄ (ORTHOCENTER), X₁₁₉ (FEUERBACH ANTIPODE), X₅₁₇ (ISOGONAL CONJUGATE OF X₁₀₄)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above X₁₅₁₂)

Search Value (6, 9, 13): \(-8.762243670773\)

▸ Incident Central Lines3 lines

{1, 4}, {119, 517}, {499, 1158}

▸ Functional Relations2 relations

• X₁₅₁₉ = reflection of X_i in X_j for these (i,j): (1512, 1532), (1532, 1538)

• X₁₅₁₉ = orthopole of PU(96)