X₃₃₀₃

INTERSECTION OF LINES X₁X_3 AND X₄₉₆X_498

X₃₃₀₃ = homothetic center of tangential triangle and reflection of extangents triangle in X₁

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

X₃₃₀₃ (INTERSECTION OF LINES X₁X_3 AND X₄₉₆X_498) 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: {1, 3}, {8, 344}

• Related Centers: X₃ (CIRCUMCENTER), X₁ (INCENTER), X₈ (NAGEL POINT), X₃₄₄ (ISOTOMIC CONJUGATE OF X₂₇₇)

Trilinears: \(3 + \cos A : 3 + \cos B : 3 + \cos C\)

Barycentrics: \((\sin A)(3 + \cos A) :(\sin B)(3 + \cos B) : (\sin C)(3 + \cos C)\)

Search Value (6, 9, 13): \(2.049853390992\)

▸ Incident Central Lines22 lines

{1, 3}, {8, 344}, {11, 1058}, {12, 497}, {42, 1191}, {145, 958}, {198, 1953}, {221, 2293}, {377, 528}, {388, 390}, {474, 551}, {495, 546}, {496, 498}, {499, 632}, {500, 1480}, {575, 613}, {576, 611}, {939, 1411}, {943, 1000}, {950, 954}, {1193, 1616}, {1201, 2177}

▸ Functional Relations4 relations

• X₃₃₀₃ = crosssum of X₁ and X₃₃₃₃

• X₃₃₀₃ = {X₁,X₄₀}-harmonic conjugate of X₃₅₄

• X₃₃₀₃ = {X₁,X₅₅}-harmonic conjugate of X₅₆

• X₃₃₀₃ = homothetic center of tangential triangle and reflection of extangents triangle in X₁