X2638

DIFFERENCE OF PU(77)

X2638 = X1-Ceva conjugate of 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) { 3, 296 }: Central Line L(3, 296) { 1, 653 }: Central Line L(1, 653) { 48, 692 }: Central Line L(48, 692) { 31, 2188 }: Central Line L(31, 2188) { 1984, 2310 }: Central Line L(1984, 2310) { 29, 2656 }: Central Line L(29, 2656) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_652 = CROSSDIFFERENCE OF X(1) AND X(4) (7.2558, -0.6836) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_296 = ISOGONAL CONJUGATE OF X(243) (0.7214, -0.0918) X_653 = TRILINEAR POLE OF LINE X(1)X(4) (0.5097, 0.6030) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_692 = -CEVA CONJUGATE OF X(101) (0.2833, 0.5715) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_2188 = -ISOCONJUGATE OF X(196) (0.6625, 1.1678) X_1984 = VEGA TRANSFORM OF X(1020) (0.4361, -0.0651) X_2310 = -ISOCONJUGATE OF X(1262) (0.7196, 0.0518) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_2656 = TRILINEAR POLE OF PU(82) (0.6337, -0.4192) X_2638 = DIFFERENCE OF PU(77) (0.6093, 0.0064) A B C X1 X652 X3 X296 X653 X48 X692 X31 X2188 X1984 X2310 X29 X2656 X2638 (a, b, c) = (5, 6, 7) | AB = 1

X2638 (DIFFERENCE OF PU(77)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/(\sec C - \sec A) - 1/(\sec B - \sec A) : :\)
Search Value (6, 9, 13): \(3.341200176027\)

X2638 lies on the incentral inellipse (i.e., Hostadter ellipse E(1/2)).

▸ Incident Central Lines7 lines

{1, 653}, {3, 296}, {29, 2656}, {31, 2188}, {48, 692}, {1984, 2310}, {2646, 2658}

▸ Functional Relations6 relations