X1578

POINT ALTERF I

X1578 = inverse-in-Brocard-circle of X1579
< 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) { 3, 6 }: Brocard Axis { 394, 488 }: Central Line L(394, 488) { 485, 1368 }: Central Line L(485, 1368) { 1040, 1124 }: Central Line L(1040, 1124) { 1038, 1335 }: Central Line L(1038, 1335) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_394 = -CEVA CONJUGATE OF X(3) (0.3778, 0.0284) X_488 = ANTICOMPLEMENT OF X(485) (0.4576, 0.0844) X_485 = VECTEN POINT (0.5773, 0.2578) X_1368 = COMPLEMENTARY CONJUGATE OF X(6) (0.4897, 0.0751) X_1040 = INTERSECTION OF LINES X(1)X(3) AND X(2)X(33) (0.4854, 0.0753) X_1124 = ISOGONAL CONJUGATE OF X(1123) (0.5846, 0.2489) X_1038 = INTERSECTION OF LINES X(1)X(3) AND X(2)X(34) (0.5104, 0.1211) X_1335 = {X(1),X(6)}-HARMONIC CONJUGATE OF X(1124) (0.4024, 0.0326) X_1578 = POINT ALTERF I (0.5127, 0.1230) A B C X3 X6 X394 X488 X485 X1368 X1040 X1124 X1038 X1335 X1578 (a, b, c) = (5, 6, 7) | AB = 1

X1578 (POINT ALTERF I) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\sin A + \sec B \sec C : \sin B + \sec C \sec B : \sin C + \sec A \sec B\)
Barycentrics: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = (\sin A)(\sin A + \sec B \sec C)\)
Search Value (6, 9, 13): \(-99.666642215841\)
▸ Incident Central Lines5 lines

{3, 6}, {394, 488}, {485, 1368}, {1038, 1335}, {1040, 1124}

▸ Functional Relations1 relation