X3294

SS(a → ab + ac) OF X3

< 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 { 21, 101 }: Central Line L(21, 101) { 190, 274 }: Central Line L(190, 274) { 573, 962 }: Central Line L(573, 962) { 672, 1125 }: Central Line L(672, 1125) { 846, 2664 }: Central Line L(846, 2664) 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_21 = SCHIFFLER POINT (0.5287, 0.1771) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_274 = ISOGONAL CONJUGATE OF X(213) (0.5168, 0.1843) X_573 = ORTHOHARMONIC OF X(58) (0.4486, 0.0172) X_962 = LONGUET-HIGGINS POINT (0.7551, 0.6582) X_672 = CROSSDIFFERENCE OF X(1) AND X(514) (1.9245, 2.2184) X_1125 = COMPLEMENT OF X(10) (0.5459, 0.2083) X_846 = 4th SHARYGIN POINT (0.5437, 0.1969) X_2664 = CROSSDIFFERENCE OF PU(84) (1.9947, 1.6278) X_3294 = SS(a → ab + ac) OF X(3) (0.5263, 0.1797) A B C X1 X6 X21 X101 X190 X274 X573 X962 X672 X1125 X846 X2664 X3294 (a, b, c) = (5, 6, 7) | AB = 1

X3294 (SS(a → ab + ac) OF X3) 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 \(f(a,b,c) = (ab + ac)[(bc + ba)^{2} + (ca + cb)^{2} - (ab + ac)^{2}]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(3.061426742157\)
▸ Incident Central Lines6 lines

{1, 6}, {21, 101}, {190, 274}, {573, 962}, {672, 1125}, {846, 2664}

▸ Functional Relations1 relation