X968

POINT ALDERAMIN

X968 = crossdifference of every pair of points on line X661X905
< 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, 21 }: Central Line L(1, 21) { 19, 25 }: Central Line L(19, 25) { 9, 42 }: Central Line L(9, 42) { 45, 210 }: Central Line L(45, 210) { 165, 750 }: Central Line L(165, 750) { 200, 756 }: Central Line L(200, 756) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_969 = INTERSECTION OF LINES X(10)X(69) AND X(19)X(81) (0.5857, 0.2544) X_1 = INCENTER (0.5714, 0.2333) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_19 = CLAWSON POINT (0.6246, 0.4244) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_9 = MITTENPUNKT (0.5110, 0.1615) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_45 = -BETH CONJUGATE OF X(1) (0.5418, 0.1981) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_750 = INTERSECTION OF LINES X(1)X(88) AND X(2)X(31) (0.5675, 0.2354) X_200 = -CEVA CONJUGATE OF X(9) (0.4392, 0.1037) X_756 = CROSSPOINT OF X(10) AND X(37) (0.5409, 0.1988) X_968 = POINT ALDERAMIN (0.5557, 0.2126) A B C X969 X1 X21 X19 X25 X9 X42 X45 X210 X165 X750 X200 X756 X968 (a, b, c) = (5, 6, 7) | AB = 1

X968 (POINT ALDERAMIN) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a^{2} - 2a(b + c) - (b + c)^{2} : :\)
Search Value (6, 9, 13): \(2.150752517522\)
▸ Alternate Coordinates1 form

  • Trilinears: \(r_{a}^{2} - sS : r_{b}^{2} - sS : r_{c}^{2} - sS\)

▸ Incident Central Lines9 lines

{1, 21}, {9, 42}, {19, 25}, {35, 975}, {45, 210}, {165, 750}, {200, 756}, {614, 1001}, {943, 1039}

▸ Functional Relations3 relations