X581

ORTHOHARMONIC OF X284

X581 = inverse-in-Brocard-circle of X580
< 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) { 1, 4 }: Incenter–Orthocenter Line { 3, 6 }: Brocard Axis { 35, 47 }: Central Line L(35, 47) { 40, 42 }: Central Line L(40, 42) { 81, 411 }: Central Line L(81, 411) { 84, 941 }: Central Line L(84, 941) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_4 = ORTHOCENTER (0.6122, 0.3958) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_47 = -BETH CONJUGATE OF X(34) (0.7279, 0.4389) X_40 = BEVAN POINT (0.4286, -0.0292) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_411 = EULER X(21)-2nd-SUBSTITUTION POINT (0.4414, -0.0514) X_84 = ISOGONAL CONJUGATE OF X(40) (0.6071, 0.6816) X_941 = ISOGONAL CONJUGATE OF X(940) (0.5671, 0.2256) X_581 = ORTHOHARMONIC OF X(284) (0.5657, 0.2106) A B C X1 X4 X3 X6 X35 X47 X40 X42 X81 X411 X84 X941 X581 (a, b, c) = (5, 6, 7) | AB = 1

X581 (ORTHOHARMONIC 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 \(D/2 = (2abc - e_{1} + e_{2})/[4 \operatorname{area} (a + b + c)]\), 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): \(2.619112999419\)
▸ Incident Central Lines10 lines

{1, 4}, {3, 6}, {35, 47}, {40, 42}, {81, 411}, {84, 941}, {222, 1035}, {936, 966}, {947, 1036}, {995, 1104}

▸ Functional Relations2 relations