X774

CROSSPOINT OF X1 AND X158

X774 is the crosspoint of X1 and X158.
< 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, 21 }: Central Line L(1, 21) { 55, 201 }: Central Line L(55, 201) { 821, 823 }: Central Line L(821, 823) { 601, 1060 }: Central Line L(601, 1060) { 602, 1062 }: Central Line L(602, 1062) { 938, 986 }: Central Line L(938, 986) 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_158 = -CROSS CONJUGATE OF X(92) (0.6215, 0.5117) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_201 = -CEVA CONJUGATE OF X(12) (0.4897, 0.1062) X_821 = ISOGONAL CONJUGATE OF X(820) (0.5996, 0.4597) X_823 = ISOGONAL CONJUGATE OF X(822) (0.5623, 0.6035) X_601 = INTERSECTION OF LINES X(3)X(31) AND X(55)X(255) (0.5761, 0.2252) X_1060 = INTERSECTION OF LINES X(1)X(3) AND X(5)X(34) (0.5181, 0.1353) X_602 = INTERSECTION OF LINES X(3)X(31) AND X(56)X(255) (0.8182, 0.6170) X_1062 = INTERSECTION OF LINES X(1)X(3) AND X(5)X(33) (0.4633, 0.0347) X_938 = ANTICOMPLEMENT OF X(936) (0.5846, 0.2462) X_986 = INTERSECTION OF LINES X(1)X(3) AND X(8)X(38) (0.5588, 0.2101) X_774 = CROSSPOINT OF X(1) AND X(158) (0.6363, 0.3186) A B C X1 X158 X21 X55 X201 X821 X823 X601 X1060 X602 X1062 X938 X986 X774 (a, b, c) = (5, 6, 7) | AB = 1

X774 (CROSSPOINT OF X1 AND X158) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\cos^{2} B + \cos^{2} C : :\)
Search Value (6, 9, 13): \(1.206397861735\)
▸ Alternate Coordinates2 forms

  • Trilinears: \(1 - \cos A \cos(B - C) : :\)

  • Trilinears: \(2 a^{2} (b^{2} - c^{2})^{2} - a^{4} (b^{2} + c^{2}) - (b^{2} - c^{2})^{2} (b^{2} + c^{2}) : :\)

▸ Incident Central Lines7 lines

{1, 21}, {55, 201}, {601, 1060}, {602, 1062}, {821, 823}, {912, 1066}, {938, 986}

▸ Functional Relations4 relations