X756

CROSSPOINT OF X10 AND X37

X756 is the crosspoint of X10 and X37.
< 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) { 2, 38 }: Central Line L(2, 38) { 9, 31 }: Central Line L(9, 31) { 37, 42 }: Central Line L(37, 42) { 45, 55 }: Central Line L(45, 55) { 12, 201 }: Central Line L(12, 201) { 10, 321 }: Central Line L(10, 321) 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_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_2 = CENTROID (0.5374, 0.2000) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_9 = MITTENPUNKT (0.5110, 0.1615) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_45 = -BETH CONJUGATE OF X(1) (0.5418, 0.1981) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_201 = -CEVA CONJUGATE OF X(12) (0.4897, 0.1062) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_756 = CROSSPOINT OF X(10) AND X(37) (0.5409, 0.1988) A B C X10 X37 X2 X38 X9 X31 X42 X45 X55 X12 X201 X321 X756 (a, b, c) = (5, 6, 7) | AB = 1

X756 (CROSSPOINT OF X10 AND X37) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((b + c)^{2} : (c + a)^{2} : (a + b)^{2}\)
Barycentrics: \(a(b + c)^{2} : b(c + a)^{2} : c(a + b)^{2}\)
Search Value (6, 9, 13): \(2.523359872236\)
▸ Incident Central Lines12 lines

{1, 748}, {2, 38}, {9, 31}, {10, 321}, {12, 201}, {37, 42}, {45, 55}, {63, 750}, {100, 846}, {171, 896}, {200, 968}, {405, 976}

▸ Functional Relations6 relations