X2998

CD(X32)

X2998 = trilinear pole of line X512X625 (the complement of the Lemoine axis)
< 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) { 6, 194 }: Central Line L(6, 194) { 42, 192 }: Central Line L(42, 192) { 25, 385 }: Central Line L(25, 385) { 193, 263 }: Central Line L(193, 263) { 69, 694 }: Central Line L(69, 694) { 1084, 1502 }: Central Line L(1084, 1502) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1613 = TCC-PERSPECTOR OF X(31) (0.7015, 0.3763) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_194 = -CEVA CONJUGATE OF X(2) (0.6989, 0.3222) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_192 = -CEVA CONJUGATE OF X(2) (CONGRUENT PARALLELIANS POINT) (0.6147, 0.2635) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_385 = -HIRST INVERSE OF X(6) (2.2863, 2.0795) X_193 = -CEVA CONJUGATE OF X(2) (0.7878, 0.4690) X_263 = ISOGONAL CONJUGATE OF X(183) (0.6298, 0.3525) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_694 = ISOGONAL CONJUGATE OF X(385) (1.0179, 0.0378) X_1084 = CROSSPOINT OF X(2) AND X(512) (0.8090, 0.1525) X_1502 = ISOGONAL CONJUGATE OF X(1501) (0.3682, 0.0896) X_2998 = CD(X(32)) (0.2505, 0.0728) A B C X1613 X6 X194 X42 X192 X25 X385 X193 X263 X69 X694 X1084 X1502 X2998 (a, b, c) = (5, 6, 7) | AB = 1

X2998 (CD(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 given just before X2979, using P = X32
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(28.563893085145\)
▸ Incident Central Lines7 lines

{6, 194}, {25, 385}, {42, 192}, {69, 694}, {193, 263}, {941, 1655}, {1084, 1502}

▸ Functional Relations10 relations