X2160

X2-ISOCONJUGATE OF X35

A construction for X2160 appears in Dasari Naga Vijay Krishna, On the Feuerbach Triangle.
< 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) { 9, 46 }: Central Line L(9, 46) { 55, 199 }: Central Line L(55, 199) { 284, 501 }: Central Line L(284, 501) { 396, 554 }: Central Line L(396, 554) { 6, 1406 }: Central Line L(6, 1406) { 395, 1081 }: Central Line L(395, 1081) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1652 = 4th EVANS PERSPECTOR (0.5899, 0.2763) X_1653 = 5th EVANS PERSPECTOR (0.6584, 0.3759) X_9 = MITTENPUNKT (0.5110, 0.1615) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_199 = -CEVA CONJUGATE OF X(6) (0.4796, 0.0487) X_284 = -CROSS CONJUGATE OF X(21) (0.5646, 0.2088) X_501 = MIQUEL ASSOCIATE OF INCENTER (0.5444, 0.1612) X_396 = MIDPOINT OF X(13) AND X(15) (0.5699, 0.2349) X_554 = (X(1),X(13))-ANSWER TO QUESTION A (0.5802, 0.2562) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1406 = -BETH CONJUGATE OF X(46) (0.6653, 0.5088) X_395 = MIDPOINT OF X(14) AND X(16) (1.3794, 1.1048) X_1081 = POINT ALPHECCA (0.6056, 0.3226) X_2160 = -ISOCONJUGATE OF X(35) (0.6185, 0.3356) A B C X1652 X1653 X9 X46 X55 X199 X284 X501 X396 X554 X6 X1406 X395 X1081 X2160 (a, b, c) = (5, 6, 7) | AB = 1

X2160 (X2-ISOCONJUGATE OF X35) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((\sin A)/(1 + 2 \cos A) : :\)
Barycentrics: \((\sin A)^{2}/(1 + 2 \cos A) : :\)
Search Value (6, 9, 13): \(0.021787866127\)
▸ Incident Central Lines14 lines

{6, 1406}, {9, 46}, {19, 1990}, {55, 199}, {56, 2164}, {65, 2174}, {284, 501}, {395, 1081}, {396, 554}, {909, 2262}, {910, 1174}, {1108, 2291}, {1400, 1989}, {1841, 2299}

▸ Functional Relations7 relations