X3724

X908com(INCENTRAL TRIANGLE)

X3724 = isogonal conjugate of X14616
< 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) { 31, 48 }: Central Line L(31, 48) { 42, 181 }: Central Line L(42, 181) { 36, 214 }: Central Line L(36, 214) { 55, 199 }: Central Line L(55, 199) { 187, 237 }: Central Line L(187, 237) { 100, 740 }: Central Line L(100, 740) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_181 = APOLLONIUS POINT (0.6163, 0.3093) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_214 = -CEVA CONJUGATE OF X(44) (0.3571, 0.3499) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_199 = -CEVA CONJUGATE OF X(6) (0.4796, 0.0487) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_237 = -LINE CONJUGATE OF X(2) (0.9894, 1.3825) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_740 = EVEN (- 1, 1) INFINITY POINT (0.9745, 0.5915) X_3724 = com(INCENTRAL TRIANGLE) (1.0944, 1.3190) A B C X31 X48 X42 X181 X36 X214 X55 X199 X187 X237 X100 X740 X3724 (a, b, c) = (5, 6, 7) | AB = 1

X3724 (X908com(INCENTRAL TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(a^{3} (b+c) \cdot (a^{2}-b^{2}+b c-c^{2}) : :\)
Search Value (6, 9, 13): \(-1.518063790031\)
▸ Linear Combinations1 combination
▸ Incident Central Lines16 lines

{1, 994}, {3, 2292}, {23, 1283}, {31, 48}, {36, 214}, {42, 181}, {55, 199}, {56, 2650}, {100, 740}, {187, 237}, {215, 2361}, {851, 1284}, {896, 3286}, {2078, 2611}, {2177, 2667}, {2198, 2200}

▸ Functional Relations1 relation

  • X3724 = isogonal conjugate of X14616