X3159

X1-CEVA CONJUGATE OF X10

X3159 = midpoint of X72 and X2901
< 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) { 72, 2901 }: Central Line L(72, 2901) { 37, 39 }: Central Line L(37, 39) { 58, 190 }: Central Line L(58, 190) { 10, 321 }: Central Line L(10, 321) { 192, 386 }: Central Line L(192, 386) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_2901 = ORTHIC-ISOGONAL CONJUGATE OF X(10) (0.8536, 0.4818) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_192 = -CEVA CONJUGATE OF X(2) (CONGRUENT PARALLELIANS POINT) (0.6147, 0.2635) X_386 = INVERSE-IN-BROCARD-CIRCLE OF X(58) (0.5912, 0.2526) X_3159 = -CEVA CONJUGATE OF X(10) (0.6452, 0.2776) A B C X72 X2901 X37 X39 X58 X190 X10 X321 X192 X386 X3159 (a, b, c) = (5, 6, 7) | AB = 1

X3159 (X1-CEVA CONJUGATE OF X10) 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 \(x : y : z\) = X1 and \(u : v : w\) = X10
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): \(-0.622428418368\)
▸ Incident Central Lines5 lines

{10, 321}, {37, 39}, {58, 190}, {72, 519}, {192, 386}

▸ Functional Relations4 relations