X₃₉₂₆

X₃₀₅₃com[INVERSE(n(TANGENTIAL TRIANGLE))]

X₃₉₂₆ = anticomplement of X₃₇₆₇

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

X₃₉₂₆ (X₃₀₅₃com[INVERSE(n(TANGENTIAL TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Circle: Circumcircle (circumcircle) — Passes through vertices A, B, C; centered at X₃ CIRCUMCENTER

• Central Lines: {2, 39}, {3, 69}

• Related Centers: X₃ (CIRCUMCENTER), X₂₂₀₇ (-ISOCONJUGATE OF X₃₂₆), X₂ (CENTROID), X₃₉ (BROCARD MIDPOINT), X₆₉ (SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE)

Trilinears: \(\cot^{2} A \csc A : :\) (Peter Moses, 1/13/2012)

Barycentrics: \(\cot^{2} A : \cot^{2} B : \cot^{2} C\)

Search Value (6, 9, 13): \(5.655390438701\)

▸ Alternate Coordinates1 form

• Barycentrics: \((b^{2} + c^{2} - a^{2})^{2} : :\)

▸ Incident Central Lines31 lines

{2, 39}, {3, 69}, {4, 325}, {5, 1007}, {20, 99}, {32, 193}, {110, 2366}, {115, 2996}, {183, 631}, {187, 439}, {264, 1217}, {276, 1502}, {304, 345}, {316, 3146}, {326, 1264}, {339, 3548}, {350, 3086}, {441, 1073}, {491, 1587}, {492, 1588}, {498, 3761}, {499, 3760}, {524, 3053}, {574, 3620}, {626, 2549}, {1078, 3523}, {1102, 3719}, {1235, 3541}, {1310, 3556}, {1909, 3085}, {2548, 3734}

▸ Functional Relations11 relations

• X₃₉₂₆ = isogonal conjugate of X₂₂₀₇

• X₃₉₂₆ = isotomic conjugate of X₃₉₃

• X₃₉₂₆ = complement of X₆₃₉₂

• X₃₉₂₆ = anticomplement of X₃₇₆₇

• X₃₉₂₆ = X₉₂-isoconjugate of X₁₉₇₄

• X₃₉₂₆ = trilinear pole of line X₅₂₀X₃₂₆₅

• X₃₉₂₆ = trilinear product of vertices of pedal triangle of X₂ reflected in X₂

• X₃₉₂₆ = pole wrt polar circle of trilinear polar of X₆₅₂₄ (line X₂₄₈₉X₂₅₀₈)

• X₃₉₂₆ = polar conjugate of X₆₅₂₄

• X₃₉₂₆ = barycentric square of X₆₉

• X₃₉₂₆ = trilinear product of vertices of X₂-anti altimedial triangle