X1020

POINT ALGEDI

X1020 = crosssum of X650 and X652
< 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, 185 }: Central Line L(1, 185) { 108, 109 }: Central Line L(108, 109) { 269, 292 }: Central Line L(269, 292) { 101, 651 }: Central Line L(101, 651) { 190, 658 }: Central Line L(190, 658) { 347, 573 }: Central Line L(347, 573) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1021 = ISOGONAL CONJUGATE OF X(1020) (24.7475, -5.0780) X_1 = INCENTER (0.5714, 0.2333) X_185 = NAGEL POINT OF THE ORTHIC TRIANGLE (0.6033, 0.1643) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_269 = ISOGONAL CONJUGATE OF X(200) (0.6369, 0.3847) X_292 = -HIRST INVERSE OF X(291) (1.0127, 0.0417) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.3048, 0.5599) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_658 = TRILINEAR POLE OF LINE X(1)X(7) (0.3795, 0.5837) X_347 = ISOTOMIC CONJUGATE OF X(280) (0.4531, -0.0404) X_573 = ORTHOHARMONIC OF X(58) (0.4583, 0.2009) X_1020 = POINT ALGEDI (0.4031, 0.5979) A B C X1021 X1 X185 X108 X109 X269 X292 X101 X651 X190 X658 X347 X573 X1020 (a, b, c) = (5, 6, 7) | AB = 1

X1020 (POINT ALGEDI) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((\cos B + \cos C)/(\cos B - \cos C) : :\)
Search Value (6, 9, 13): \(0.063021389965\)
▸ Incident Central Lines9 lines

{1, 185}, {57, 1086}, {101, 651}, {108, 109}, {190, 658}, {269, 292}, {347, 573}, {648, 1021}, {653, 2637}

▸ Functional Relations5 relations

Notes

Let X be a point on the Euler line. Let P and U be the 1st and 2nd bicentrics of X. As X varies, the bicentric sum of P and U trace the line X42X65, of which X1020 is the trilinear pole. (Randy Hutson, March 25, 2016)