X3307

ISOGONAL CONJUGATE OF X1381

As the isogonal conjugate of a point on the circumcircle, X3307 lies on the line at infinity.
< 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) { 30, 511 }: Central Line L(30, 511) { 100, 1381 }: Central Line L(100, 1381) { 104, 1382 }: Central Line L(104, 1382) { 11, 2446 }: Central Line L(11, 2446) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1381 = 1st INTERCEPT OF LINE X(1)X(3) AND CIRCUMCIRCLE (0.7440, 0.5503) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_1382 = 2nd INTERCEPT OF LINE X(1)X(3) AND CIRCUMCIRCLE (0.2560, -0.3461) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_2446 = 1st INTERSECTION(LINE X(1)X(3), INCIRCLE) (0.4599, 0.0284) X_3307 = ISOGONAL CONJUGATE OF X(1381) (1.1187, 0.2809) A B C X1381 X30 X511 X100 X104 X1382 X11 X2446 X3307 (a, b, c) = (5, 6, 7) | AB = 1

X3307 (ISOGONAL CONJUGATE OF X1381) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/x : 1/y : 1/z\), where \(x : y : z\) = X1381
Barycentrics: \(a/x : b/y : c/z\), where \(x : y : z\) = X1381
▸ Incident Central Lines4 lines

{11, 2446}, {30, 511}, {100, 1381}, {104, 1382}

▸ Functional Relations1 relation

Notes

The asymptotes of the Feuerbach hyperbola meet the infinity line in X3307 and X3308. See the note at X2574.