X1927

TRILINEAR POLE OF PU(13)

X1927 = cevapoint of X1932 and X1933
< 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) { 82, 662 }: Central Line L(82, 662) { 172, 694 }: Central Line L(172, 694) { 715, 805 }: Central Line L(715, 805) { 733, 787 }: Central Line L(733, 787) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1932 = CROSSSUM OF PU(14) (0.6266, 0.3438) X_1933 = CROSSDIFFERENCE OF PU(14) (0.8524, 0.7964) X_82 = ISOGONAL CONJUGATE OF X(38) (0.5943, 0.2703) X_662 = TRILINEAR POLE OF LINE X(1)X(21) (0.1811, 0.4951) X_172 = TRILINEAR PRODUCT X(6)*X(171) (0.6080, 0.2866) X_694 = ISOGONAL CONJUGATE OF X(385) (1.0179, 0.0378) X_715 = EVEN (- 3, - 1) CIRCUMCIRCLE POINT (1.0000, 0.2040) X_805 = o-(- 2, 2) CIRCUMCIRCLE POINT (0.9729, -0.0897) X_733 = EVEN (- 2, 2) CIRCUMCIRCLE POINT (1.0071, 0.0450) X_787 = o-(- 3, - 1) CIRCUMCIRCLE POINT (0.1963, 0.5122) X_1927 = TRILINEAR POLE OF PU(13) (0.9865, 0.0569) A B C X1932 X1933 X82 X662 X172 X694 X715 X805 X733 X787 X1927 (a, b, c) = (5, 6, 7) | AB = 1

X1927 (TRILINEAR POLE OF PU(13)) 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 \(f(a,b,c) = a^{4}/(a^{4} - b^{2}c^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.035958192116\)
▸ Incident Central Lines4 lines

{82, 662}, {172, 694}, {715, 805}, {733, 787}

▸ Functional Relations2 relations