X1253

ISOGONAL CONJUGATE OF X1088

X1253 is the isogonal conjugate of X1088.
< 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, 31 }: Central Line L(6, 31) { 35, 255 }: Central Line L(35, 255) { 9, 294 }: Central Line L(9, 294) { 165, 269 }: Central Line L(165, 269) { 238, 390 }: Central Line L(238, 390) { 220, 480 }: Central Line L(220, 480) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_255 = ISOGONAL CONJUGATE OF X(158) (0.4217, 0.0365) X_9 = MITTENPUNKT (0.5110, 0.1615) X_294 = ISOGONAL CONJUGATE OF X(241) (0.9276, -0.0575) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_269 = ISOGONAL CONJUGATE OF X(200) (0.6369, 0.3847) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_390 = REFLECTION OF GERGONNE POINT IN INCENTER (0.5526, 0.1897) X_220 = -CEVA CONJUGATE OF X(55) (0.4826, 0.1278) X_480 = -CEVA CONJUGATE OF X(220) (0.4089, 0.0793) X_1253 = ISOGONAL CONJUGATE OF X(1088) (0.5237, 0.1548) A B C X55 X41 X6 X31 X35 X255 X9 X294 X165 X269 X238 X390 X220 X480 X1253 (a, b, c) = (5, 6, 7) | AB = 1

X1253 (ISOGONAL CONJUGATE OF X1088) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a^{2}(b + c - a)^{2} : b^{2}(c + a - b)^{2} : c^{2}(a + b - c)^{2} = \cos^{4} A/2 : \cos^{4} B/2 : \cos^{4} C/2\)
Search Value (6, 9, 13): \(3.184172824917\)
▸ Incident Central Lines14 lines

{1, 1170}, {3, 1037}, {6, 31}, {9, 294}, {33, 756}, {35, 255}, {38, 1040}, {40, 1254}, {48, 692}, {165, 269}, {219, 949}, {220, 480}, {238, 390}, {497, 748}

▸ Functional Relations5 relations