X580

ORTHOGONAL OF X284

X580 = inverse-in-Brocard-circle of X581
< 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 { 31, 40 }: Central Line L(31, 40) { 34, 46 }: Central Line L(34, 46) { 36, 54 }: Central Line L(36, 54) { 1, 201 }: Central Line L(1, 201) { 2, 283 }: Central Line L(2, 283) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_270 = ISOGONAL CONJUGATE OF X(201) (0.6168, 0.3881) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_40 = BEVAN POINT (0.4286, -0.0292) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_54 = KOSNITA POINT (0.5880, 0.2176) X_201 = -CEVA CONJUGATE OF X(12) (0.4897, 0.1062) X_2 = CENTROID (0.5374, 0.2000) X_283 = -CROSS CONJUGATE OF X(21) (0.4475, 0.0704) X_580 = ORTHOGONAL OF X(284) (0.7089, 0.4470) A B C X270 X1 X3 X6 X31 X40 X34 X46 X36 X54 X201 X2 X283 X580 (a, b, c) = (5, 6, 7) | AB = 1

X580 (ORTHOGONAL OF X284) 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 \(f(A,B,C) = \sin A + \cot D/2 \cos A\), cot \(D/2 = (e_{1} - e_{2} - 2abc)/[4 \operatorname{area} (a + b + c)]\), where \(e_{1}\), \(e_{2}\) are as for X579
Barycentrics: \((\sin A)f(A,B,C): (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-2.718036865689\)
▸ Incident Central Lines12 lines

{1, 201}, {2, 283}, {3, 6}, {31, 40}, {34, 46}, {36, 54}, {57, 255}, {162, 412}, {165, 601}, {223, 603}, {238, 946}, {517, 595}

▸ Functional Relations4 relations