X3316

ISOGONAL CONJUGATE OF X3311

X3316 is the isogonal conjugate of X3311.
< 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) { 4, 590 }: Central Line L(4, 590) { 485, 631 }: Central Line L(485, 631) { 3, 1131 }: Central Line L(3, 1131) { 5, 1132 }: Central Line L(5, 1132) { 226, 1374 }: Central Line L(226, 1374) { 376, 1327 }: Central Line L(376, 1327) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1587 = POINT CASTOR I (0.6026, 0.2943) X_4 = ORTHOCENTER (0.6122, 0.3958) X_590 = ISOGONAL CONJUGATE OF X(588) (0.5615, 0.2258) X_485 = VECTEN POINT (0.5773, 0.2578) X_631 = 3/5*OG (0.5224, 0.1608) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1131 = ARCTAN(2) KIEPERT POINT (0.5904, 0.2888) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_1132 = ARCTAN(-2) KIEPERT POINT (0.8864, -0.3774) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_1374 = 2nd GRIFFITHS POINT (0.5977, 0.2940) X_376 = CENTROID OF THE ANTIPEDAL TRIANGLE OF X(2) (0.4626, 0.0042) X_1327 = ARCTAN(3) KIEPERT POINT (0.5967, 0.3083) X_3316 = ISOGONAL CONJUGATE OF X(3311) (0.5639, 0.2341) A B C X1587 X4 X590 X485 X631 X3 X1131 X5 X1132 X226 X1374 X376 X1327 X3316 (a, b, c) = (5, 6, 7) | AB = 1

X3316 (ISOGONAL CONJUGATE OF X3311) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/(\cos A + 2 \sin A) : 1/(\cos B + 2 \sin B) : 1/(\cos C + 2 \sin C)\)
Barycentrics: \((\sin A)/(\cos A + 2 \sin A) : (\sin B)/(\cos B + 2 \sin B) : (\sin C) /(\cos C + 2 \sin C)\)
Search Value (6, 9, 13): \(1.509856104371\)
▸ Alternate Coordinates1 form

  • Trilinears: \(\sec(A - t) : \sec(B - t) : \sec(C - t)\), where t = arctan(2)

▸ Incident Central Lines7 lines

{3, 1131}, {4, 590}, {5, 1132}, {6, 3317}, {226, 1374}, {376, 1327}, {485, 631}

▸ Functional Relations3 relations