X1598

POINT CHERTAN II

X1598 = orthocentroidal-circle-inverse of X1595
< 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) { 2, 3 }: Euler Line { 154, 578 }: Central Line L(154, 578) { 34, 999 }: Central Line L(34, 999) { 1, 1057 }: Central Line L(1, 1057) { 51, 1181 }: Central Line L(51, 1181) { 155, 1351 }: Central Line L(155, 1351) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_4 = ORTHOCENTER (0.6122, 0.3958) X_154 = -CEVA CONJUGATE OF X(6) (0.4807, -0.3954) X_578 = ORTHOHARMONIC OF X(216) (0.5933, 0.2561) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_999 = MIDPOINT OF X(1) AND X(57) (0.5926, 0.2722) X_1 = INCENTER (0.5714, 0.2333) X_1057 = ISOGONAL CONJUGATE OF X(1056) (0.5671, 0.2170) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_1181 = 2nd SARAGOSSA POINT OF X(3) (0.5894, 0.1559) X_155 = EIGENCENTER OF ORTHIC TRIANGLE (1.1658, 0.5033) X_1351 = REFLECTION OF X(3) IN X(6) (0.7000, 0.4324) X_1598 = POINT CHERTAN II (0.6217, 0.4204) A B C X2 X3 X4 X154 X578 X34 X999 X1 X1057 X51 X1181 X155 X1351 X1598 (a, b, c) = (5, 6, 7) | AB = 1

X1598 (POINT CHERTAN II) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\cos A - 2 \sec A : :\)
Search Value (6, 9, 13): \(-2.446476820174\)
▸ Incident Central Lines8 lines

{1, 1057}, {2, 3}, {34, 999}, {51, 1181}, {154, 578}, {155, 1351}, {389, 1498}, {399, 1112}

▸ Functional Relations5 relations

Notes

As a point on the Euler line, X1598 has Shinagawa coefficients \((F, -2E - F)\).