X3510

INTERSECTION OF LINES X1X_76 AND X6X_43

< 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, 43 }: Central Line L(6, 43) { 1, 76 }: Central Line L(1, 76) { 291, 511 }: Central Line L(291, 511) { 42, 894 }: Central Line L(42, 894) { 292, 2238 }: Central Line L(292, 2238) { 1402, 1423 }: Central Line L(1402, 1423) 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_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_1 = INCENTER (0.5714, 0.2333) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_291 = 2nd SHARYGIN POINT (1.0249, 0.0364) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_894 = ISOGONAL CONJUGATE OF X(893) (0.5501, 0.2184) X_292 = -HIRST INVERSE OF X(291) (1.0127, 0.0417) X_2238 = -ISOCONJUGATE OF X(741) (2.2505, 2.0410) X_1402 = -BETH CONJUGATE OF X(42) (0.6396, 0.3585) X_1423 = -BETH CONJUGATE OF X(192) (0.6537, 0.3692) X_3510 = INTERSECTION OF LINES X(1)X(76) AND X(6)X(43) (1.7132, 1.1732) A B C X6 X43 X1 X76 X291 X511 X42 X894 X292 X2238 X1402 X1423 X3510 (a, b, c) = (5, 6, 7) | AB = 1

X3510 (INTERSECTION OF LINES X1X_76 AND X6X_43) 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 \(f(a,b,c) = b^{3}c^{3} - a^{3}b^{3} - a^{3}c^{3} + a^{2}b^{2}c^{2} (E\). Danneels)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-4.098442511153\)

X3510 lies on the cubic Z(X385).

▸ Incident Central Lines9 lines

{1, 76}, {6, 43}, {42, 894}, {291, 511}, {292, 2238}, {1402, 1423}, {1492, 1933}, {3225, 3507}, {3505, 3512}

▸ Functional Relations1 relation