X920

X158-CEVA CONJUGATE OF X1

X920 = isogonal conjugate of X921
< 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) { 4, 46 }: Central Line L(4, 46) { 4, 78 }: Central Line L(4, 78) { 19, 91 }: Central Line L(19, 91) { 9, 498 }: Central Line L(9, 498) { 57, 499 }: Central Line L(57, 499) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_158 = -CROSS CONJUGATE OF X(92) (0.6215, 0.5117) X_1 = INCENTER (0.5714, 0.2333) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_4 = ORTHOCENTER (0.6122, 0.3958) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_19 = CLAWSON POINT (0.6246, 0.4244) X_91 = ISOGONAL CONJUGATE OF X(47) (-0.0865, -0.0205) X_9 = MITTENPUNKT (0.5110, 0.1615) X_498 = YFF CONCURRENT CONGRUENT CIRCLES POINT (0.5518, 0.2140) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_499 = {X(1),X(2)}-HARMONIC CONJUGATE OF X(498) (0.4458, 0.1102) X_920 = -CEVA CONJUGATE OF X(1) (0.8006, 0.5344) A B C X158 X1 X21 X4 X46 X78 X19 X91 X9 X498 X57 X499 X920 (a, b, c) = (5, 6, 7) | AB = 1

X920 (X158-CEVA CONJUGATE OF X1) 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 \(f(A,B,C) = \cos^{2} B + \cos^{2} C - \cos^{2} A\)
Search Value (6, 9, 13): \(0.064033621130\)
▸ Alternate Coordinates2 forms

  • Trilinears: \(S_{A} - 2 R^{2} : :\)

  • Trilinears: \(a^{6} - 3 a^{4} (b^{2} + c^{2}) + a^{2} (3 b^{4} - 2 b^{2} c^{2} + 3 c^{4}) - (b^{2} - c^{2})^{2} (b^{2} + c^{2}) : :\)

▸ Incident Central Lines9 lines

{1, 21}, {4, 46}, {4, 78}, {9, 498}, {19, 91}, {57, 499}, {158, 921}, {201, 601}, {243, 1075}

▸ Functional Relations2 relations