X3553

INTERSECTION OF LINES X1X_6 AND X19X_41

X3553 = {X1,X6}-harmonic conjugate of X3554
< 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 { 19, 41 }: Central Line L(19, 41) { 33, 42 }: Central Line L(33, 42) { 65, 198 }: Central Line L(65, 198) { 172, 577 }: Central Line L(172, 577) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3554 = INTERSECTION OF LINES X(1)X(6) AND X(19)X(604) (0.6589, 0.3371) X_1 = INCENTER (0.5714, 0.2333) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_19 = CLAWSON POINT (0.6246, 0.4244) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_198 = -CEVA CONJUGATE OF X(6) (0.4741, -0.0381) X_172 = TRILINEAR PRODUCT X(6)*X(171) (0.6080, 0.2866) X_577 = HARMONIC OF X(216) (0.4663, 0.0464) X_3553 = INTERSECTION OF LINES X(1)X(6) AND X(19)X(41) (0.5885, 0.2536) A B C X3554 X1 X6 X19 X41 X33 X42 X65 X198 X172 X577 X3553 (a, b, c) = (5, 6, 7) | AB = 1

X3553 (INTERSECTION OF LINES X1X_6 AND X19X_41) 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 \(f(A,B,C) = \sin A + \sin A \sin B \sin C\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(1.158913265239\)
▸ Alternate Coordinates2 forms

  • Trilinears: \(aR + rs : bR + rs : cR + rs\)

  • Trilinears: \(a^{2}bc + S^{2} : b^{2}ca + S^{2} : c^{2}ab + S^{2}\)

▸ Incident Central Lines31 lines

{1, 6}, {19, 41}, {33, 42}, {34, 3087}, {35, 1609}, {48, 2285}, {57, 2178}, {65, 198}, {71, 1182}, {78, 2345}, {165, 1030}, {172, 577}, {200, 594}, {205, 1474}, {216, 1040}, {284, 1766}, {326, 894}, {380, 584}, {571, 609}, {610, 2174}, {612, 2318}, {800, 1500}, {1490, 1901}, {1834, 2910}, {1953, 2082}, {2099, 2262}, {2266, 2294}, {2270, 3340}, {2303, 2327}, {3068, 3084}, {3069, 3083}

▸ Functional Relations1 relation