X₂₁₆₇

X₂-ISOCONJUGATE OF X₅₁

X₂₁₆₇ = isogonal conjugate of X₁₉₅₃

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

X₂₁₆₇ (X₂-ISOCONJUGATE OF X₅₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {54, 72}, {48, 92}

• Related Centers: X₁₉₅₃ (BICENTRIC SUM OF PU(21)), X₅₄ (KOSNITA POINT), X₇₂ (ISOGONAL CONJUGATE OF X₂₈), X₄₈ (CROSSPOINT OF X₁ AND X₆₃), X₉₂ (CEVAPOINT OF INCENTER AND CLAWSON POINT)

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X₅₁

Barycentrics: \(\sec(B - C) : :\)

Search Value (6, 9, 13): \(-13.491425094632\)

▸ Alternate Coordinates2 forms

• Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = 1/(\sin(2B) + \sin(2C))\) (Randy Hutson, 9/23/2011)

• Trilinears: \(1/(a^{2} (b^{2} + c^{2}) - (b^{2} - c^{2})^{2}) : :\)

▸ Incident Central Lines10 lines

{1, 1748}, {38, 293}, {48, 92}, {54, 72}, {63, 2148}, {75, 2168}, {95, 306}, {97, 1214}, {162, 1954}, {226, 275}

▸ Functional Relations7 relations

• X₂₁₆₇ = isogonal conjugate of X₁₉₅₃

• X₂₁₆₇ = isotomic conjugate of X₁₄₂₁₃

• X₂₁₆₇ = cevapoint of X_i and X_j for these (i,j): (1, 48), (2148, 2169)

• X₂₁₆₇ = X_i-cross conjugate of X_j for these (i,j): (48, 2169), (822, 162), (1577, 662), (2148, 2190)

• X₂₁₆₇ = X₅-isoconjugate of X₆

• X₂₁₆₇ = trilinear pole of line X₆₅₆X₁₉₅₅

• X₂₁₆₇ = crosspoint of X₁ and X₄₈ wrt excentral triangle