X3247

INTERSECTION OF LINES X1X_6 AND X2X_2321

X3247 = crosssum of X6 and X3303
< 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, 6 }: Incenter–Symmedian Line { 226, 347 }: Central Line L(226, 347) { 519, 966 }: Central Line L(519, 966) { 574, 988 }: Central Line L(574, 988) { 902, 968 }: Central Line L(902, 968) { 579, 1334 }: Central Line L(579, 1334) 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_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_347 = ISOTOMIC CONJUGATE OF X(280) (0.4531, -0.0404) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_966 = INTERSECTION OF LINES X(2)X(6) AND X(4)X(9) (0.5191, 0.1803) X_574 = HARMONIC OF X(187) (0.5539, 0.1910) X_988 = INTERSECTION OF LINES X(1)X(3) AND X(9)X(39) (0.5598, 0.2120) X_902 = CROSSPOINT OF X(6) AND X(106) (1.2500, 1.2247) X_968 = POINT ALDERAMIN (0.5557, 0.2126) X_579 = HARMONIC OF X(284) (0.7212, 0.4674) X_1334 = POINT ALYA (0.5324, 0.1760) X_3247 = INTERSECTION OF LINES X(1)X(6) AND X(2)X(2321) (0.5631, 0.2234) A B C X1 X6 X226 X347 X519 X966 X574 X988 X902 X968 X579 X1334 X3247 (a, b, c) = (5, 6, 7) | AB = 1

X3247 (INTERSECTION OF LINES X1X_6 AND X2X_2321) 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 \(f(a,b,c) = a + 3b + 3c\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.914416828688\)
▸ Incident Central Lines13 lines

{1, 6}, {2, 2321}, {187, 2959}, {226, 347}, {281, 1886}, {519, 966}, {574, 988}, {579, 1334}, {594, 1698}, {612, 1962}, {902, 968}, {1068, 1826}, {1255, 1796}

▸ Functional Relations3 relations