X₃₆₇₉

X₃₅₇₆com(EXTOUCH TRIANGLE)

X₃₆₇₉ = midpoint of X₂ and X₈

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

X₃₆₇₉ (X₃₅₇₆com(EXTOUCH TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 8}

• Related Centers: X₂ (CENTROID), X₈ (NAGEL POINT)

Trilinears: \(3 r - 4 R \sin B \sin C : :\)

Barycentrics: \(a - 2b - 2c : :\)

Search Value (6, 9, 13): \(3.568429075520\)

▸ Linear Combinations1 combination

• X₃₆₇₉ = X₁ - \(2\) X₂ = X₈ + \(2\) X₁₀

▸ Incident Central Lines48 lines

{1, 2}, {5, 3657}, {9, 80}, {12, 3340}, {30, 40}, {35, 958}, {36, 956}, {46, 529}, {63, 484}, {75, 537}, {100, 993}, {140, 3654}, {148, 1654}, {165, 376}, {210, 381}, {333, 3550}, {341, 1089}, {388, 553}, {516, 3543}, {518, 599}, {524, 3416}, {527, 1478}, {536, 984}, {540, 1046}, {542, 2948}, {544, 1282}, {549, 952}, {730, 3097}, {752, 1757}, {944, 3524}, {946, 3545}, {966, 2321}, {982, 1739}, {996, 1150}, {1213, 3247}, {1377, 3299}, {1378, 3301}, {1479, 2551}, {1573, 2276}, {1574, 2275}, {1697, 1837}, {1743, 2345}, {1768, 3359}, {1788, 3361}, {3208, 3294}, {3434, 3583}, {3436, 3585}, {3534, 3579}

▸ Functional Relations16 relations

• X₃₆₇₉ = midpoint of X₂ and X₈

• X₃₆₇₉ = reflection of X₁ in X₂

• X₃₆₇₉ = isogonal conjugate of X₂₁₆₃

• X₃₆₇₉ = isotomic conjugate of complement of X₁₇₄₈₈

• X₃₆₇₉ = isotomic conjugate of anticomplement of X₁₆₅₉₀

• X₃₆₇₉ = complement of X₃₂₄₁

• X₃₆₇₉ = anticomplement of X₅₅₁

• X₃₆₇₉ = {X₈,X₁₀}-harmonic conjugate of X₁

• X₃₆₇₉ = harmonic center of incircle and Spieker circle

• X₃₆₇₉ = harmonic center of Conway circle and excircles radical circle

• X₃₆₇₉ = X₁₆₅com[Inverse(n(Hexyl))]

• X₃₆₇₉ = homothetic center of Caelum triangle and cross-triangle of Aquila and anti-Aquila triangles

• X₃₆₇₉ = outer-Garcia-to-ABC similarity image of X₂

• X₃₆₇₉ = reflection of X₂ in X₁₀

• X₃₆₇₉ = excentral-to-ABC barycentric image of X₃₅₇₆

• X₃₆₇₉ = homothetic center of Gemini triangle 20 and cross-triangle of Gemini triangles 20 and 28