X1361

BRISSE TRANSFORM OF X104

X1361 = reflection of X1364 in X3
< 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) { 1364, 3 }: Central Line L(1364, 3) { 11, 65 }: Central Line L(11, 65) { 12, 124 }: Central Line L(12, 124) { 55, 102 }: Central Line L(55, 102) { 56, 106 }: Central Line L(56, 106) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1364 = BRISSE TRANSFORM OF X(108) (0.5367, 0.6071) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_124 = -OF-MEDIAL-TRIANGLE (0.6243, 0.0030) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_102 = Λ(INCENTER, ORTHOCENTER) (0.6364, -0.3897) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_1361 = BRISSE TRANSFORM OF X(104) (0.5091, 0.4581) A B C X1364 X3 X11 X65 X12 X124 X55 X102 X56 X106 X1361 (a, b, c) = (5, 6, 7) | AB = 1

X1361 (BRISSE TRANSFORM OF X104) 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) is as above X1354, using X = X104
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.181149139197\)

X1361 lies on the incircle.

▸ Incident Central Lines10 lines

{1, 1364}, {11, 65}, {12, 124}, {55, 102}, {56, 106}, {151, 497}, {181, 994}, {928, 1362}, {962, 1118}, {1122, 1358}

▸ Functional Relations6 relations