X1104

CROSSPOINT OF X1 AND X28

X1104 is the midpoint of the bicentric pair \(y : z : x\) and \(z : x : y\), where \(x : y : z\) = X72
< 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) { 1, 6 }: Incenter–Symmedian Line { 25, 34 }: Central Line L(25, 34) { 31, 65 }: Central Line L(31, 65) { 11, 429 }: Central Line L(11, 429) { 229, 593 }: Central Line L(229, 593) { 32, 910 }: Central Line L(32, 910) 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_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_429 = EULER X(58)-5th-SUBSTITUTION POINT (0.6024, 0.3700) X_229 = -CEVA CONJUGATE OF X(81) (0.5961, 0.2991) X_593 = 1st HATZIPOLAKIS-YIU POINT (0.6202, 0.3026) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_910 = CROSSPOINT OF X(57) AND X(105) (1.3163, 2.5495) X_1104 = CROSSPOINT OF X(1) AND X(28) (0.6311, 0.3042) A B C X1 X28 X6 X25 X34 X31 X65 X11 X429 X229 X593 X32 X910 X1104 (a, b, c) = (5, 6, 7) | AB = 1

X1104 (CROSSPOINT OF X1 AND X28) 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 \(f(a,b,c) = 2avw + cv^{2} + bw^{2} + u(bv + cw)\),\(u : v : w\) = X72
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(0.545886518628\)
▸ Incident Central Lines14 lines

{1, 6}, {11, 429}, {25, 34}, {31, 65}, {32, 910}, {58, 942}, {81, 1098}, {105, 961}, {210, 976}, {229, 593}, {239, 1043}, {440, 950}, {517, 580}, {581, 995}

▸ Functional Relations3 relations