X3977

X902com[INVERSE(n(TANGENTIAL TRIANGLE))]

X3977 = isogonal conjugate of X8752
< 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) circumcircle: Circumcircle of △ABC { 63, 69 }: Central Line L(63, 69) { 441, 525 }: Central Line L(441, 525) { 190, 908 }: Central Line L(190, 908) { 519, 902 }: Central Line L(519, 902) { 2, 2415 }: Central Line L(2, 2415) { 100, 2751 }: Central Line L(100, 2751) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_441 = COMPLEMENT OF X(297) (0.3841, -0.2011) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0468, 0.2556) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_908 = POINT ACUBENS (-0.8367, -1.7996) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_902 = CROSSPOINT OF X(6) AND X(106) (1.2500, 1.2247) X_2 = CENTROID (0.5374, 0.2000) X_2415 = GIBERT-SIMSON TRANSFORM OF X(1293) (-0.1531, -0.1500) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_2751 = SR(X(105), X(109)) (-0.0078, 0.1527) X_3977 = com[INVERSE(n(TANGENTIAL TRIANGLE))] (-0.1531, -0.1500) A B C X3 X63 X69 X441 X525 X190 X908 X519 X902 X2 X2415 X100 X2751 X3977 (a, b, c) = (5, 6, 7) | AB = 1

X3977 (X902com[INVERSE(n(TANGENTIAL TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) :f(c,a,b)\), where \(f(a,b,c) = (b + c - 2a)(b^{2} + c^{2} - a^{2})\)
Search Value (6, 9, 13): \(5.952238239696\)
▸ Incident Central Lines15 lines

{2, 2415}, {3, 3710}, {63, 69}, {100, 2751}, {110, 2760}, {190, 908}, {344, 3306}, {441, 525}, {516, 3006}, {518, 3712}, {519, 902}, {726, 3011}, {1150, 2321}, {3219, 3687}, {3589, 3666}

▸ Functional Relations3 relations