X3198

X40-CEVA CONJUGATE OF X71

X3198 = crosspoint of X20 and X610
< 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) { 19, 25 }: Central Line L(19, 25) { 40, 64 }: Central Line L(40, 64) { 42, 65 }: Central Line L(42, 65) { 10, 440 }: Central Line L(10, 440) { 100, 1297 }: Central Line L(100, 1297) { 12, 1869 }: Central Line L(12, 1869) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_40 = BEVAN POINT (0.4286, -0.0292) X_71 = ISOGONAL CONJUGATE OF X(27) (0.4807, 0.0915) X_19 = CLAWSON POINT (0.6246, 0.4244) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_64 = ISOGONAL CONJUGATE OF X(20) (0.5579, 1.5943) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_440 = COMPLEMENT OF X(27) (0.4970, 0.0943) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_1297 = COLLINGS TRANSFORM OF X(127) (0.4838, -0.4080) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_1869 = ZOSMA TRANSFORM OF X(405) (0.6206, 0.4150) X_3198 = -CEVA CONJUGATE OF X(71) (0.4129, -0.2261) A B C X40 X71 X19 X25 X64 X42 X65 X10 X440 X100 X1297 X12 X1869 X3198 (a, b, c) = (5, 6, 7) | AB = 1

X3198 (X40-CEVA CONJUGATE OF X71) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(u(-u/x + v/y + w/z) : v(u/x - v/y + w/z) : w(u/x + v/y - w/z)\), where \(x : y : z\) = X40 and \(u : v : w\) = X71
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\), where \(f(a,b,c) = u(-u/x + v/y + w/z)\)
Search Value (6, 9, 13): \(-60.059126641909\)
▸ Incident Central Lines15 lines

{10, 440}, {12, 1869}, {19, 25}, {31, 2264}, {40, 64}, {42, 65}, {100, 1297}, {204, 3172}, {210, 1903}, {212, 2182}, {517, 3190}, {1011, 1212}, {1071, 1715}, {1108, 2352}, {1260, 1766}

▸ Functional Relations3 relations