X₉₃₆

INTERSECTION OF LINES X₁X_2 AND X₃X_9

X₉₃₆ = complement of X₉₃₈

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

X₉₃₆ (INTERSECTION OF LINES X₁X_2 AND X₃X_9) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Derived Triangle: Medial Triangle △M_aM_bM_c — vertices M_a, M_b, M_c (Formed by the midpoints of sides BC, CA, AB)

• Central Lines: {2, 938}

• Related Centers: X₂ (CENTROID), X₉₃₈ (ANTICOMPLEMENT OF X₉₃₆)

Trilinears: \(a^{3} - a^{2}(b + c) - a(b - c)^{2} + (b + c)^{3} : :\)

Search Value (6, 9, 13): \(3.184010137905\)

▸ Incident Central Lines13 lines

{1, 2}, {3, 9}, {40, 960}, {56, 210}, {57, 72}, {63, 404}, {165, 411}, {223, 1038}, {226, 443}, {269, 307}, {377, 908}, {581, 966}, {984, 988}

▸ Functional Relations4 relations

• X₉₃₆ = isogonal conjugate of X₉₃₇

• X₉₃₆ = complement of X₉₃₈

• X₉₃₆ = exsimilicenter of hexyl and Spieker circles; the insimilicenter is X₉₆₂₃

• X₉₃₆ = homothetic center of medial triangle and tangential triangle of the hexyl triangle