X3158

X1-CEVA CONJUGATE OF X9

X3158 = crosssum of X513 and X3020
< 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) { 9, 55 }: Central Line L(9, 55) { 57, 100 }: Central Line L(57, 100) { 1, 474 }: Central Line L(1, 474) { 165, 518 }: Central Line L(165, 518) { 31, 678 }: Central Line L(31, 678) { 41, 728 }: Central Line L(41, 728) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_9 = MITTENPUNKT (0.5110, 0.1615) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_474 = EULER LINE INTERCEPT OF LINE X(10)X(56) (0.5441, 0.2176) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_678 = CROSSPOINT OF X(1) AND X(44) (0.3571, 0.3499) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_728 = INTERSECTION OF LINES X(8)X(9) AND X(57)X(345) (0.3648, 0.0624) X_3158 = -CEVA CONJUGATE OF X(9) (0.6726, 0.2916) A B C X1 X9 X55 X57 X100 X474 X165 X518 X31 X678 X41 X728 X3158 (a, b, c) = (5, 6, 7) | AB = 1

X3158 (X1-CEVA CONJUGATE OF X9) 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 \(f(a,b,c) = (b + c - a)(b + c - 3a)\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-3.155242550986\)
▸ Incident Central Lines15 lines

{1, 474}, {9, 55}, {31, 678}, {40, 758}, {41, 728}, {42, 1449}, {57, 100}, {78, 1697}, {145, 1420}, {165, 518}, {528, 1699}, {612, 1962}, {1743, 3052}, {1998, 2078}, {2340, 3208}

▸ Functional Relations7 relations