X1220

ISOGONAL CONJUGATE OF X1193

X1220 is the isogonal conjugate of X1193.
< 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) { 2, 12 }: Central Line L(2, 12) { 6, 8 }: Central Line L(6, 8) { 10, 58 }: Central Line L(10, 58) { 34, 92 }: Central Line L(34, 92) { 1, 312 }: Central Line L(1, 312) { 65, 257 }: Central Line L(65, 257) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1193 = 3rd SARAGOSSA POINT OF X(1) (0.5959, 0.2573) X_2 = CENTROID (0.5374, 0.2000) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_8 = NAGEL POINT (0.4694, 0.1333) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_1 = INCENTER (0.5714, 0.2333) X_312 = ISOTOMIC CONJUGATE OF X(57) (0.4256, 0.1081) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_257 = ISOGONAL CONJUGATE OF X(172) (0.5240, 0.1822) X_1220 = ISOGONAL CONJUGATE OF X(1193) (0.5436, 0.2094) A B C X1193 X2 X12 X6 X8 X10 X58 X34 X92 X1 X312 X65 X257 X1220 (a, b, c) = (5, 6, 7) | AB = 1

X1220 (ISOGONAL CONJUGATE OF X1193) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/f(a,b,c) : 1/f(b,c,a) : 1/f(c,a,b)\), where f(a,b,c) is as in X1193
Search Value (6, 9, 13): \(2.434362991817\)
▸ Incident Central Lines13 lines

{1, 312}, {2, 12}, {6, 8}, {10, 58}, {34, 92}, {42, 1043}, {65, 257}, {85, 269}, {86, 313}, {106, 1125}, {292, 1107}, {341, 612}, {519, 1126}

▸ Functional Relations9 relations