X₃₃₀₉

ISOGONAL CONJUGATE OF X₁₂₉₂

As the isogonal conjugate of a point on the circumcircle, X₃₃₀₉ lies on the line at infinity.

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

X₃₃₀₉ (ISOGONAL CONJUGATE OF X₁₂₉₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {30, 511}, {3, 667}

• Related Centers: X₁₂₉₂ (COLLINGS TRANSFORM OF X₅₅), X₃₀ (EULER INFINITY POINT), X₅₁₁ (ISOGONAL CONJUGATE OF X₉₈), X₃ (CIRCUMCENTER), X₆₆₇ (CROSSDIFFERENCE OF X₂ AND X₃₇)

Trilinears: \((b - c)(a^{2} + b^{2} + c^{2} - 2ab - 2ac) : :\)

▸ Incident Central Lines24 lines

{1, 3669}, {3, 667}, {4, 885}, {30, 511}, {74, 2752}, {98, 2711}, {99, 2704}, {100, 2742}, {101, 2736}, {102, 2751}, {103, 2725}, {104, 840}, {109, 2730}, {110, 2691}, {218, 2440}, {644, 1292}, {650, 1734}, {663, 905}, {764, 1482}, {1293, 2748}, {1294, 2749}, {1295, 2750}, {1296, 2753}, {1297, 2754}

▸ Functional Relations6 relations

• X₃₃₀₉ = isogonal conjugate of X₁₂₉₂

• X₃₃₀₉ = ideal point of PU(44)

• X₃₃₀₉ = bicentric difference of PU(44)

• X₃₃₀₉ = Thomson-isogonal conjugate of X₁₀₅

• X₃₃₀₉ = Lucas-isogonal conjugate of X₁₀₅

• X₃₃₀₉ = Cundy-Parry Psi transform of X₁₄₂₆₇