X3700

X661com(EXTOUCH TRIANGLE)

X3700 = perspector of hyperbola {{A, B, C,X8,X10}}
< 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) { 37, 647 }: Central Line L(37, 647) { 9, 1021 }: Central Line L(9, 1021) { 321, 850 }: Central Line L(321, 850) { 522, 650 }: Central Line L(522, 650) { 523, 661 }: Central Line L(523, 661) { 649, 900 }: Central Line L(649, 900) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_647 = CROSSDIFFERENCE OF X(2) AND X(3) (4.2063, -0.5653) X_9 = MITTENPUNKT (0.5110, 0.1615) X_1021 = ISOGONAL CONJUGATE OF X(1020) (24.7475, -5.0780) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_850 = BARYCENTRIC MULTIPLIER FOR KIEPERT HYPERBOLA (-6.8003, 1.7304) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (13.7143, -4.1991) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_661 = CROSSDIFFERENCE OF X(1) AND X(21) (48.4286, -23.0952) X_649 = CROSSDIFFERENCE OF X(1) and X(2) (-21.0000, 14.6969) X_900 = CROSSDIFFERENCE OF X(6) AND X(101) (0.9566, 0.6107) X_3700 = com(EXTOUCH TRIANGLE) (-29.2653, 6.5986) A B C X37 X647 X9 X1021 X321 X850 X522 X650 X523 X661 X649 X900 X3700 (a, b, c) = (5, 6, 7) | AB = 1

X3700 (X661com(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 \(f(a,b,c) = (b + c - a)(b^{2} - c^{2})\)
Search Value (6, 9, 13): \(66.109843925431\)
▸ Incident Central Lines14 lines

{9, 1021}, {37, 647}, {101, 2689}, {321, 850}, {424, 2501}, {522, 650}, {523, 661}, {525, 1577}, {649, 900}, {693, 918}, {824, 3004}, {1635, 2490}, {2533, 3566}, {3910, 4391}

▸ Functional Relations6 relations