X3715

X3305com(EXTOUCH TRIANGLE)

X3715 = excentral-to-ABC barycentric image of X3305
< 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) { 9, 55 }: Central Line L(9, 55) { 42, 45 }: Central Line L(42, 45) { 44, 612 }: Central Line L(44, 612) { 6, 756 }: Central Line L(6, 756) { 10, 1836 }: Central Line L(10, 1836) { 940, 1757 }: Central Line L(940, 1757) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_9 = MITTENPUNKT (0.5110, 0.1615) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_45 = -BETH CONJUGATE OF X(1) (0.5418, 0.1981) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_612 = INTERSECTION OF LINES X(1)X(2) AND X(9)X(31) (0.5582, 0.2203) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_756 = CROSSPOINT OF X(10) AND X(37) (0.5409, 0.1988) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_1836 = ZOSMA TRANSFORM OF X(33) (0.6066, 0.3254) X_940 = POINT ALDEBARAN (0.5757, 0.2411) X_1757 = MIMOSA TRANSFORM OF X(295) (2.6667, 2.7217) X_3715 = com(EXTOUCH TRIANGLE) (0.5036, 0.1555) A B C X9 X55 X42 X45 X44 X612 X6 X756 X10 X1836 X940 X1757 X3715 (a, b, c) = (5, 6, 7) | AB = 1

X3715 (X3305com(EXTOUCH TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(b + c - a)(2b + 2c + a)\)
Search Value (6, 9, 13): \(3.731071207315\)
▸ Incident Central Lines11 lines

{6, 756}, {8, 3058}, {9, 55}, {10, 1836}, {42, 45}, {44, 612}, {518, 3305}, {748, 3242}, {940, 1757}, {960, 2098}, {1376, 3219}

▸ Functional Relations1 relation

  • X3715 = excentral-to-ABC barycentric image of X3305