X2667

SUM OF PU(85)

X2667 = trilinear pole, wrt incentral triangle, of Lemoine axis
< 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, 75 }: Central Line L(1, 75) { 37, 42 }: Central Line L(37, 42) { 192, 714 }: Central Line L(192, 714) { 284, 922 }: Central Line L(284, 922) { 55, 2305 }: Central Line L(55, 2305) { 518, 2292 }: Central Line L(518, 2292) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2292 = -ISOCONJUGATE OF X(1169) (0.5509, 0.2064) X_1 = INCENTER (0.5714, 0.2333) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_192 = -CEVA CONJUGATE OF X(2) (CONGRUENT PARALLELIANS POINT) (0.6147, 0.2635) X_714 = EVEN (- 3, - 1) INFINITY POINT (1.0302, 0.5186) X_284 = -CROSS CONJUGATE OF X(21) (0.5646, 0.2088) X_922 = POINT ALBALI (0.9307, 0.9656) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_2305 = -ISOCONJUGATE OF X(1247) (0.6601, 0.3665) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_2667 = SUM OF PU(85) (0.5803, 0.2413) A B C X2292 X1 X75 X37 X42 X192 X714 X284 X922 X55 X2305 X518 X2667 (a, b, c) = (5, 6, 7) | AB = 1

X2667 (SUM OF PU(85)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(ca/(c + a) + ba/(b + a) : :\)
Search Value (6, 9, 13): \(1.464576757972\)
▸ Incident Central Lines11 lines

{1, 75}, {37, 42}, {55, 2305}, {190, 2663}, {192, 714}, {284, 922}, {518, 2292}, {798, 2670}, {1100, 2309}, {2293, 2650}, {2294, 2643}

▸ Functional Relations6 relations