X1353

REFLECTION OF X5 IN X6

X1353 is the reflection of X5 in X6.
< 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) { 5, 6 }: Nine-Point–Symmedian Line { 3, 193 }: Central Line L(3, 193) { 69, 140 }: Central Line L(69, 140) { 182, 524 }: Central Line L(182, 524) { 141, 575 }: Central Line L(141, 575) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_193 = -CEVA CONJUGATE OF X(2) (0.7878, 0.4690) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_140 = MIDPOINT OF X(3) AND X(5) (0.5281, 0.1755) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5500, 0.1846) X_524 = ISOGONAL CONJUGATE OF X(111) (0.1376, -0.2297) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_575 = ORTHOGONAL OF X(187) (0.5750, 0.2259) X_1353 = REFLECTION OF X(5) IN X(6) (0.6439, 0.2855) A B C X5 X6 X3 X193 X69 X140 X182 X524 X141 X575 X1353 (a, b, c) = (5, 6, 7) | AB = 1

X1353 (REFLECTION OF X5 IN X6) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = 2a - R \cos(B-C) \cot \omega\)
Barycentrics: \(4 a^{6} - 7 a^{4} (b^{2} + c^{2}) + 4 a^{2} (b^{4} - b^{2} c^{2} + c^{4}) - (b^{2} - c^{2})^{2} (b^{2} + c^{2}) : :\)
Search Value (6, 9, 13): \(1.432945248496\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = 4 \sin A - \cos(B - C) \cot \omega\)

▸ Incident Central Lines8 lines

{3, 193}, {5, 6}, {30, 1351}, {69, 140}, {141, 575}, {182, 524}, {511, 550}, {542, 3845}

▸ Functional Relations2 relations