X2909

ORTHIC-ISOGONAL CONJUGATE OF X32

X2909 is the orthic-isogonal conjugate of X32.
< 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) { 5, 182 }: Central Line L(5, 182) { 39, 184 }: Central Line L(39, 184) { 211, 571 }: Central Line L(211, 571) { 76, 2001 }: Central Line L(76, 2001) { 512, 1968 }: Central Line L(512, 1968) { 1692, 1974 }: Central Line L(1692, 1974) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5500, 0.1846) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_211 = -CEVA CONJUGATE OF X(39) (0.6801, 0.4536) X_571 = ORTHOHARMONIC OF X(52) (0.7141, 0.4556) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_2001 = ORTHOCORRESPONDENT OF X(32) (0.4984, 0.2475) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_1968 = CROSSSUM OF PU(37) (0.5947, 0.4354) X_1692 = RADICAL TRACE OF CIRCUMCIRCLE AND 2nd LEMOINE CIRCLE (0.7995, 0.5968) X_1974 = BARYCENTRIC PRODUCT OF PU(39) (0.6402, 0.4907) X_2909 = ORTHIC-ISOGONAL CONJUGATE OF X(32) (0.5750, 0.4473) A B C X4 X32 X5 X182 X39 X184 X211 X571 X76 X2001 X512 X1968 X1692 X1974 X2909 (a, b, c) = (5, 6, 7) | AB = 1

X2909 (ORTHIC-ISOGONAL CONJUGATE OF X32) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where f(a,b,c) is as described just before X2883
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.164194197078\)
▸ Incident Central Lines6 lines

{5, 182}, {39, 184}, {76, 2001}, {211, 571}, {512, 1968}, {1692, 1974}

▸ Functional Relations3 relations