X1083

MIDPOINT OF X105 AND X644

X1083 is the midpoint of X105 and X644.
< 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) { 105, 644 }: Central Line L(105, 644) { 1, 6 }: Incenter–Symmedian Line { 3, 667 }: Central Line L(3, 667) { 8, 1016 }: Central Line L(8, 1016) { 55, 1026 }: Central Line L(55, 1026) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_644 = TRILINEAR MULTIPLIER FOR YFF PARABOLA (-0.0171, 0.3359) X_1 = INCENTER (0.5714, 0.2333) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_667 = CROSSDIFFERENCE OF X(2) AND X(37) (-6.1667, 5.7155) X_8 = NAGEL POINT (0.4694, 0.1333) X_1016 = -CROSS CONJUGATE OF X(99) (0.3832, 0.2666) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_1026 = INTERSECTION OF LINES X(1)X(2) AND X(100)X(101) (4.1429, 3.7326) X_1083 = MIDPOINT OF X(105) AND X(644) (0.4771, 0.1213) A B C X105 X644 X1 X6 X3 X667 X8 X1016 X55 X1026 X1083 (a, b, c) = (5, 6, 7) | AB = 1

X1083 (MIDPOINT OF X105 AND X644) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a^{4} - a^{3}(b + c) - a^{2}bc + 2abc(b + c) - bc(b^{2} + c^{2}): :L\)
Search Value (6, 9, 13): \(6.125336725977\)

X1083 lies on a circle related to the 1st and 2nd Brocard points; Hyacinthos message #4053, Paul Yiu, Oct. 4, 2001. X1083 lies on the Brocard circle.

X1083 lies on the Brocard circle, the circle O(1,3).

▸ Incident Central Lines7 lines

{1, 6}, {3, 667}, {8, 1016}, {55, 1026}, {56, 1025}, {105, 644}, {840, 898}

▸ Functional Relations11 relations