X₃₉₂₅

X₁₀₀₆com[INVERSE(n(HEXYL TRIANGLE))]

Let A'B'C' be the intouch triangle of the extangents triangle, if ABC is acute. Then A'B'C' is homothetic to the medial triangle at X₃₉₂₅. (Randy Hutson, December 2, 2017)

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

X₃₉₂₅ (X₁₀₀₆com[INVERSE(n(HEXYL 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: {2, 11}, {10, 12}

• Related Centers: X₁ (INCENTER), X₂ (CENTROID), X₁₁ (FEUERBACH POINT), X₁₀ (SPIEKER CENTER), X₁₂ ({X)

Barycentrics: \((b + c)(b^{2} + c^{2} - ab - ac - 2bc) : :\)

Search Value (6, 9, 13): \(2.627995753955\)

▸ Incident Central Lines33 lines

{2, 11}, {5, 40}, {8, 3475}, {9, 1836}, {10, 12}, {19, 427}, {38, 1086}, {56, 443}, {71, 1213}, {75, 3703}, {125, 3611}, {141, 3779}, {142, 354}, {306, 3696}, {329, 3715}, {377, 958}, {429, 1869}, {495, 3679}, {496, 3624}, {516, 3683}, {594, 2294}, {612, 3772}, {756, 3120}, {858, 3101}, {908, 3740}, {984, 3782}, {1212, 1855}, {1329, 2476}, {1738, 3666}, {1842, 1883}, {1853, 3197}, {1859, 1861}, {3189, 3616}