X1357

BRISSE TRANSFORM OF X100

X1357 = X107-of-intouch triangle
< A B C >: Reference Triangle △ABC < T_a T_b T_c >: Intouch (Contact) Triangle △T_a T_b T_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) incircle: Incircle of △ABC [ T_a X_1357 ]: Line [ T_a X_1357 ] [ T_b X_1357 ]: Line [ T_b X_1357 ] [ T_c X_1357 ]: Line [ T_c X_1357 ] { 43, 57 }: Central Line L(43, 57) { 12, 121 }: Central Line L(12, 121) { 56, 106 }: Central Line L(56, 106) { 55, 1293 }: Central Line L(55, 1293) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) T_a = Incircle Touchpoint T_a on BC (0.7673, 0.3599) T_b = Incircle Touchpoint T_b on CA (0.4082, 0.3999) T_c = Incircle Touchpoint T_c on AB (0.5714, 0.0000) X_1 = INCENTER (0.5714, 0.2333) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_121 = -OF-MEDIAL-TRIANGLE (0.3061, 0.2999) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_1293 = COLLINGS TRANSFORM OF X(121) (0.0000, 0.2041) X_1357 = BRISSE TRANSFORM OF X(100) (0.8000, 0.1866) A B C Ta Tb Tc X1 X43 X57 X12 X121 X56 X106 X55 X1293 X1357 (a, b, c) = (5, 6, 7) | AB = 1

X1357 (BRISSE TRANSFORM OF X100) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a (b + c - a) (b - c)^{2} (a^{2} - (b - c)^{2})^{2} : :\)
Search Value (6, 9, 13): \(0.237951926922\)

X1357 lies on the incircle.

▸ Incident Central Lines6 lines

{12, 121}, {43, 57}, {55, 1293}, {56, 106}, {65, 1317}, {1086, 1365}

▸ Functional Relations10 relations