X978

X56-CEVA CONJUGATE OF X1

X978 = isogonal conjugate of X979
< 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, 2 }: Nagel Line { 9, 39 }: Central Line L(9, 39) { 58, 87 }: Central Line L(58, 87) { 3, 238 }: Central Line L(3, 238) { 31, 404 }: Central Line L(31, 404) { 266, 361 }: Central Line L(266, 361) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_9 = MITTENPUNKT (0.5110, 0.1615) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_87 = -CROSS CONJUGATE OF X(1) (0.4794, 0.1691) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_404 = {X(2),X(3)}-HARMONIC CONJUGATE OF X(21) (0.5538, 0.2429) X_266 = ISOGONAL CONJUGATE OF X(188) (0.6074, 0.2891) X_361 = -CEVA CONJUGATE OF X(1) (0.6578, 0.3310) X_978 = -CEVA CONJUGATE OF X(1) (0.7456, 0.4040) A B C X56 X1 X2 X9 X39 X58 X87 X3 X238 X31 X404 X266 X361 X978 (a, b, c) = (5, 6, 7) | AB = 1

X978 (X56-CEVA CONJUGATE OF X1) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a^{2}(b + c) + a(b^{2} - bc + c^{2}) - bc(b + c) : :\)
Search Value (6, 9, 13): \(-1.226595555535\)
▸ Alternate Coordinates1 form

  • Trilinears: \(\csc^{2}(B/2) + \csc^{2}(C/2) - \csc^{2}(A/2) : :\)

▸ Incident Central Lines16 lines

{1, 2}, {3, 238}, {9, 39}, {21, 748}, {31, 404}, {40, 1050}, {46, 1054}, {56, 979}, {57, 1046}, {58, 87}, {72, 982}, {171, 474}, {266, 361}, {631, 1064}, {651, 1106}, {960, 986}

▸ Functional Relations3 relations