X3253

INTERSECTION OF X6X_190 AND X238X_874

< 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) { 6, 190 }: Central Line L(6, 190) { 238, 874 }: Central Line L(238, 874) { 727, 789 }: Central Line L(727, 789) { 2, 2109 }: Central Line L(2, 2109) { 765, 2209 }: Central Line L(765, 2209) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_874 = INTERSECTION OF LINES X(1)X(75) AND X(99)X(670) (-2.0525, -2.1172) X_727 = EVEN (- 2, -1) CIRCUMCIRCLE POINT (1.0060, 0.1685) X_789 = o-(- 3, 0) CIRCUMCIRCLE POINT (0.0826, 0.3957) X_2 = CENTROID (0.5374, 0.2000) X_2109 = -ISOCONJUGATE OF X(2108) (-0.0481, 0.7903) X_765 = CEVAPOINT OF X(1) AND X(100) (0.4286, 0.3110) X_2209 = -ISOCONJUGATE OF X(330) (0.6618, 0.3583) X_3253 = INTERSECTION OF X(6)X(190) AND X(238)X(874) (0.4274, 0.3108) A B C X6 X190 X238 X874 X727 X789 X2 X2109 X765 X2209 X3253 (a, b, c) = (5, 6, 7) | AB = 1

X3253 (INTERSECTION OF X6X_190 AND X238X_874) 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 \(f(a,b,c) = bc(a^{2} - bc)/(b^{2}c - b^{2}a + c^{2}b - c^{2}a)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.423987124329\)
▸ Incident Central Lines5 lines

{2, 2109}, {6, 190}, {238, 874}, {727, 789}, {765, 2209}