X227

X10-CEVA CONJUGATE OF X65

X227 = X10-Ceva conjugate of X65
< 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) { 12, 37 }: Central Line L(12, 37) { 34, 55 }: Central Line L(34, 55) { 42, 65 }: Central Line L(42, 65) { 56, 197 }: Central Line L(56, 197) { 40, 221 }: Central Line L(40, 221) { 46, 222 }: Central Line L(46, 222) 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_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_197 = -CEVA CONJUGATE OF X(6) (0.4333, -0.1633) X_40 = BEVAN POINT (0.4286, -0.0292) X_221 = -CEVA CONJUGATE OF X(56) (0.5474, -0.0688) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_222 = -CEVA CONJUGATE OF X(56) (0.5653, 0.1568) X_227 = -CEVA CONJUGATE OF X(65) (0.4792, -0.0460) A B C X10 X65 X12 X37 X34 X55 X42 X56 X197 X40 X221 X46 X222 X227 (a, b, c) = (5, 6, 7) | AB = 1

X227 (X10-CEVA CONJUGATE OF X65) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (b + c)(\cos B + \cos C - \cos A - 1)\tan A/2\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-1.308770722861\)
▸ Incident Central Lines10 lines

{12, 37}, {34, 55}, {40, 221}, {42, 65}, {46, 222}, {56, 197}, {198, 208}, {201, 210}, {322, 347}, {607, 910}

▸ Functional Relations6 relations