X3678

X5com(EXTOUCH TRIANGLE)

X3678 = X1125-of-inner-Garcia 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) { 8, 80 }: Central Line L(8, 80) { 100, 191 }: Central Line L(100, 191) { 1, 748 }: Central Line L(1, 748) { 9, 943 }: Central Line L(9, 943) { 517, 546 }: Central Line L(517, 546) 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_8 = NAGEL POINT (0.4694, 0.1333) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_191 = -CEVA CONJUGATE OF X(1) (0.4859, 0.1209) X_1 = INCENTER (0.5714, 0.2333) X_748 = INTERSECTION OF LINES X(2)X(31) AND X(9)X(38) (0.4360, 0.0802) X_9 = MITTENPUNKT (0.5110, 0.1615) X_943 = ISOGONAL CONJUGATE OF X(942) (0.5528, 0.2043) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_546 = MIDPOINT OF X(4) AND X(5) (0.5842, 0.3223) X_3678 = com(EXTOUCH TRIANGLE) (0.4786, 0.1283) A B C X10 X12 X8 X80 X100 X191 X1 X748 X9 X943 X517 X546 X3678 (a, b, c) = (5, 6, 7) | AB = 1

X3678 (X5com(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 \(f(a,b,c) = a(b + c)(- a^{2} + b^{2} + c^{2} + bc)\)
Search Value (6, 9, 13): \(4.383485244254\)
▸ Linear Combinations1 combination
▸ Incident Central Lines31 lines

{1, 748}, {3, 2801}, {8, 80}, {9, 943}, {10, 12}, {35, 3219}, {38, 3216}, {58, 1757}, {78, 993}, {100, 191}, {200, 1005}, {214, 2975}, {386, 872}, {392, 3244}, {502, 594}, {517, 546}, {518, 1125}, {519, 960}, {537, 596}, {551, 3555}, {668, 1237}, {740, 3159}, {762, 2295}, {765, 1098}, {936, 1445}, {942, 3635}, {956, 1388}, {976, 1724}, {997, 1420}, {2292, 3293}, {3057, 3625}

▸ Functional Relations2 relations