X1869

ZOSMA TRANSFORM OF X405

< 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) { 4, 9 }: Orthocenter–Spieker Line { 28, 35 }: Central Line L(28, 35) { 34, 42 }: Central Line L(34, 42) { 65, 225 }: Central Line L(65, 225) { 27, 306 }: Central Line L(27, 306) { 209, 1829 }: Central Line L(209, 1829) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_9 = MITTENPUNKT (0.5110, 0.1615) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_225 = -CEVA CONJUGATE OF X(65) (0.6246, 0.4451) X_27 = CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER (0.6182, 0.4112) X_306 = ISOTOMIC CONJUGATE OF X(27) (0.3924, 0.0579) X_209 = -CEVA CONJUGATE OF X(37) (0.7303, 0.4592) X_1829 = ZOSMA TRANSFORM OF X(10) (0.6233, 0.4161) X_1869 = ZOSMA TRANSFORM OF X(405) (0.6206, 0.4150) A B C X4 X9 X28 X35 X34 X42 X65 X225 X27 X306 X209 X1829 X1869 (a, b, c) = (5, 6, 7) | AB = 1

X1869 (ZOSMA TRANSFORM OF X405) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: (y + z) sec A : (z + x) sec B : (x + y) sec C,\(x : y : z\) = X405
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X405
Search Value (6, 9, 13): \(-2.100683381672\)
▸ Incident Central Lines9 lines

{4, 9}, {27, 306}, {28, 35}, {34, 42}, {65, 225}, {209, 1829}, {210, 1868}, {1710, 1770}, {1859, 1894}