X1359

BRISSE TRANSFORM OF X102

X1359 = X1299-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_1359 ]: Line [ T_a X_1359 ] [ T_b X_1359 ]: Line [ T_b X_1359 ] [ T_c X_1359 ]: Line [ T_c X_1359 ] { 4, 11 }: Central Line L(4, 11) { 12, 123 }: Central Line L(12, 123) { 55, 1295 }: Central Line L(55, 1295) { 269, 1358 }: Central Line L(269, 1358) 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_4 = ORTHOCENTER (0.6122, 0.3958) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_123 = -OF-MEDIAL-TRIANGLE (0.5401, -0.0057) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_1295 = COLLINGS TRANSFORM OF X(123) (0.4680, -0.4072) X_269 = ISOGONAL CONJUGATE OF X(200) (0.6369, 0.3847) X_1358 = BRISSE TRANSFORM OF X(101) (0.7869, 0.1440) X_1359 = BRISSE TRANSFORM OF X(102) (0.5861, 0.4661) A B C Ta Tb Tc X1 X4 X11 X12 X123 X55 X1295 X269 X1358 X1359 (a, b, c) = (5, 6, 7) | AB = 1

X1359 (BRISSE TRANSFORM OF X102) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

  • Derived Triangle: Intouch (Contact) Triangle △TaTbTc — vertices Ta, Tb, Tc (Contact triangle of Incircle touchpoints on BC, CA, AB)

  • Circle: Incircle (incircle) — Inscribed circle tangent to sidelines at T_a, T_b, T_c; centered at X1 INCENTER

  • Concurrence Lines: Ta–X1359, Tb–X1359, Tc–X1359 concurring at X1359

  • Related Centers: X1 (INCENTER)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where f(a,b,c) is as above X1354, using X = X102
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.125835887900\)

X1359 lies on the incircle.

▸ Incident Central Lines6 lines

{1, 3318}, {4, 11}, {12, 123}, {55, 1295}, {65, 1364}, {269, 1358}

▸ Functional Relations3 relations