X3983

X3523com(EXTOUCH 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) { 10, 12 }: Central Line L(10, 12) { 354, 1698 }: Central Line L(354, 1698) { 936, 1319 }: Central Line L(936, 1319) { 37, 3214 }: Central Line L(37, 3214) { 1, 3711 }: Central Line L(1, 3711) { 8, 3740 }: Central Line L(8, 3740) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_354 = WEILL POINT (0.5823, 0.2533) X_1698 = INSIMILICENTER(BEVAN CIRCLE, NINE-POINTCIRCLE) (0.5306, 0.1933) X_936 = INTERSECTION OF LINES X(1)X(2) AND X(3)X(9) (0.5138, 0.1768) X_1319 = BEVAN-SCHRÖDER POINT (0.9524, 0.9331) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_3214 = -CEVA CONJUGATE OF X(37) (0.7124, 0.3714) X_1 = INCENTER (0.5714, 0.2333) X_3711 = com(EXTOUCH TRIANGLE) (0.4744, 0.1320) X_8 = NAGEL POINT (0.4694, 0.1333) X_3740 = com[n(INCENTRAL)*n(MEDIAL)] (0.5150, 0.1733) X_3983 = com(EXTOUCH TRIANGLE) (0.5085, 0.1676) A B C X10 X12 X354 X1698 X936 X1319 X37 X3214 X1 X3711 X8 X3740 X3983 (a, b, c) = (5, 6, 7) | AB = 1

X3983 (X3523com(EXTOUCH TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(b + c)(b^{2} + c^{2} - a^{2} + 6bc)\)
Search Value (6, 9, 13): \(3.465923594076\)
▸ Incident Central Lines14 lines

{1, 3711}, {8, 3740}, {10, 12}, {37, 3214}, {40, 3715}, {354, 1698}, {392, 3626}, {405, 3689}, {518, 3619}, {936, 1319}, {960, 3617}, {3057, 3679}, {3555, 3634}, {3696, 3701}