X3225

SS(a → bc) OF X98

X3225 = Steiner-circumellipse-X6-antipode of X670
< 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) { 32, 99 }: Central Line L(32, 99) { 6, 670 }: Central Line L(6, 670) { 729, 886 }: Central Line L(729, 886) { 190, 1918 }: Central Line L(190, 1918) { 648, 1974 }: Central Line L(648, 1974) { 290, 2422 }: Central Line L(290, 2422) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3229 = ISOGONAL CONJUGATE OF X(3225) (1.6061, 1.0091) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_99 = STEINER POINT (0.1109, 0.4322) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_670 = TRILINEAR POLE OF LINE X(2)X(39) (-0.0057, 0.2948) X_729 = EVEN (- 2, 0) CIRCUMCIRCLE POINT (1.0096, 0.1290) X_886 = INTERSECTION OF LINES X(99)X(669) AND X(512)X(670) (0.7371, -0.1549) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_1918 = BICENTRIC SUM OF PU(12) (0.6333, 0.3163) X_648 = TRILINEAR POLE OF EULER LINE (0.4563, 0.5855) X_1974 = BARYCENTRIC PRODUCT OF PU(39) (0.6402, 0.4907) X_290 = ISOGONAL CONJUGATE OF X(237) (0.7829, -0.1380) X_2422 = ISOGONAL CONJUGATE OF X(2396) (1.0041, 0.1128) X_3225 = SS(a → bc) OF X(98) (1.1195, 0.2435) A B C X3229 X32 X99 X6 X670 X729 X886 X190 X1918 X648 X1974 X290 X2422 X3225 (a, b, c) = (5, 6, 7) | AB = 1

X3225 (SS(a → bc) OF X98) 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 \(f(a,b,c) = bc/(a^{2}b^{4} + a^{2}c^{4} - b^{2}c^{4} - c ^{2}b^{4})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-2.603791810720\)
▸ Alternate Coordinates1 form

  • Trilinears: for X3225 are obtained by applying the symbolic substitution (a,b,c) → (bc,ca,ab) to trilinear coordinates of X98. As a symbolic substitution, this mapping takes circumconics to circumconics. In particular, it maps circumcircle onto the Steiner circumellipse, which passes through X3225.

X3225 lies on the Steiner circumellipse.

▸ Incident Central Lines6 lines

{6, 670}, {32, 99}, {190, 1918}, {290, 2422}, {648, 1974}, {729, 886}

▸ Functional Relations6 relations