X3818

X1352com(EULER TRIANGLE)

X3818 = intersection of Fermat axes of ABC and 1st Brocard triangle
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 6, 13 }: Central Line L(6, 13) { 4, 69 }: Central Line L(4, 69) { 30, 141 }: Central Line L(30, 141) { 5, 182 }: Central Line L(5, 182) { 147, 262 }: Central Line L(147, 262) { 302, 383 }: Central Line L(302, 383) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) X_4 = ORTHOCENTER (0.6122, 0.3958) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5500, 0.1846) X_147 = TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE (-0.1660, 1.0561) X_262 = ISOGONAL CONJUGATE OF X(182) (0.5893, 0.2856) X_302 = ISOTOMIC CONJUGATE OF 1st NAPOLEON POINT (0.5043, 0.1643) X_383 = EULER LINE INTERCEPT OF LINE X(14)X(98) (1.5441, 2.8340) X_3818 = com(EULER TRIANGLE) (0.5622, 0.3132) A B C X6 X13 X4 X69 X30 X141 X5 X182 X147 X262 X302 X383 X3818 (a, b, c) = (5, 6, 7) | AB = 1

X3818 (X1352com(EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(b^{6} + c^{6} - a^{6} - b^{4}c^{2} - b^{2}c^{4} - 2a^{2}b^{2}c^{2} : :\)
Search Value (6, 9, 13): \(-2.781892211361\)
▸ Alternate Coordinates1 form

  • Barycentrics: \(S_{A}^{2} (S_{B} + S_{C}) + S_{B} S_{C} (4 S_{A} + 3 S_{B} + 3 S_{C}) : :\)

▸ Incident Central Lines24 lines

{2, 1495}, {3, 2916}, {4, 69}, {5, 182}, {6, 13}, {30, 141}, {98, 3407}, {125, 1995}, {147, 262}, {302, 383}, {303, 1080}, {343, 428}, {376, 3619}, {382, 1350}, {403, 1974}, {546, 576}, {575, 3091}, {1469, 3585}, {1539, 2781}, {1619, 1853}, {3056, 3583}, {3060, 3410}, {3543, 3620}, {3545, 3618}

▸ Functional Relations7 relations

  • X3818 = intersection of Fermat axes of ABC and 1st Brocard triangle

  • X3818 = inverse-in-Kiepert-hyperbola of X5309

  • X3818 = X7-of-Ehrmann-vertex-triangle if ABC is acute

  • X3818 = X6-of-Ehrmann-mid-triangle

  • X3818 = {X13,X14}-harmonic conjugate of X5309

  • X3818 = perspector of Ehrmann vertex-triangle and Ehrmann mid-triangle

  • X3818 = intersection, other than X4, of the Brocard circles of the 1st and 2nd Ehrmann circumscribing triangles