X1967

TRILINEAR POLE OF PU(36)

X1967 = cevapoint of X1580 and X1582
< 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) { 256, 291 }: Central Line L(256, 291) { 42, 694 }: Central Line L(42, 694) { 38, 799 }: Central Line L(38, 799) { 213, 904 }: Central Line L(213, 904) { 733, 813 }: Central Line L(733, 813) { 741, 805 }: Central Line L(741, 805) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1966 = CROSSDIFFERENCE OF PU(36) (-93.0476, -83.6296) X_256 = 1st SHARYGIN POINT (0.5601, 0.2146) X_291 = 2nd SHARYGIN POINT (1.0249, 0.0364) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_694 = ISOGONAL CONJUGATE OF X(385) (1.0179, 0.0378) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_799 = ISOGONAL CONJUGATE OF X(798) (0.0470, 0.3636) X_213 = -CEVA CONJUGATE OF X(42) (0.6135, 0.2833) X_904 = -HIRST INVERSE OF X(256) (0.6163, 0.2816) X_733 = EVEN (- 2, 2) CIRCUMCIRCLE POINT (1.0071, 0.0450) X_813 = o-(- 1, 1) CIRCUMCIRCLE POINT (0.9721, -0.0916) X_741 = EVEN (- 1, 1) CIRCUMCIRCLE POINT (1.0071, 0.0451) X_805 = o-(- 2, 2) CIRCUMCIRCLE POINT (0.9729, -0.0897) X_1967 = TRILINEAR POLE OF PU(36) (1.0067, 0.0434) A B C X1966 X256 X291 X42 X694 X38 X799 X213 X904 X733 X813 X741 X805 X1967 (a, b, c) = (5, 6, 7) | AB = 1

X1967 (TRILINEAR POLE OF PU(36)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a^{2}/(a^{4} - b^{2}c^{2})\)
Search Value (6, 9, 13): \(-0.086113174534\)
▸ Incident Central Lines8 lines

{1, 1581}, {38, 799}, {42, 694}, {213, 904}, {256, 291}, {733, 813}, {741, 805}, {875, 881}

▸ Functional Relations7 relations