X₃₆₆₇

X₅₁₃com(INTOUCH TRIANGLE)

X₃₆₆₇ = excentral-isogonal conjugate of X₁₀₅₄

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

X₃₆₆₇ (X₅₁₃com(INTOUCH TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Circle: Incircle (incircle) — Inscribed circle tangent to sidelines at T_a, T_b, T_c; centered at X₁ INCENTER

• Central Lines: {30, 511}, {4, 2457}

• Related Centers: X₁ (INCENTER), X₁₂₉₃ (COLLINGS TRANSFORM OF X₁₂₁), X₃₀ (EULER INFINITY POINT), X₅₁₁ (ISOGONAL CONJUGATE OF X₉₈), X₄ (ORTHOCENTER), X₂₄₅₇ (RADICAL CENTER OF {ORTHOCENTROIDAL, BEVAN, FUHRMANN} CIRCLES)

Barycentrics: \((b - c)(3a - b - c) : :\)

▸ Linear Combinations1 combination

• X₃₆₆₇ = X₅₁₃com(Hexyl) = X₅₁₃com(Excentral)

▸ Incident Central Lines26 lines

{4, 2457}, {30, 511}, {74, 2758}, {98, 2712}, {99, 2705}, {100, 2743}, {101, 2737}, {102, 2757}, {103, 2726}, {104, 2718}, {109, 2731}, {110, 2692}, {145, 2403}, {572, 1919}, {649, 3239}, {885, 3062}, {1027, 1721}, {1292, 2748}, {1294, 2755}, {1295, 2756}, {1296, 2759}, {1297, 2760}, {1519, 1769}, {1768, 2957}, {2394, 3429}, {2487, 2496}

▸ Functional Relations5 relations

• X₃₆₆₇ = isogonal conjugate of X₁₂₉₃

• X₃₆₆₇ = isotomic conjugate of isogonal conjugate of X₈₆₄₃

• X₃₆₆₇ = excentral-isogonal conjugate of X₁₀₅₄

• X₃₆₆₇ = Thomson-isogonal conjugate of X₁₀₆

• X₃₆₆₇ = Lucas-isogonal conjugate of X₁₀₆