X1046

X65-CEVA CONJUGATE OF X1

X1046 = X65-Ceva conjugate of X1
< 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, 21 }: Central Line L(1, 21) { 43, 46 }: Central Line L(43, 46) { 72, 171 }: Central Line L(72, 171) { 40, 511 }: Central Line L(40, 511) { 10, 894 }: Central Line L(10, 894) { 6, 986 }: Central Line L(6, 986) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_1 = INCENTER (0.5714, 0.2333) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_171 = {X(2), X(31)}-HARMONIC CONJUGATE OF X(238) (0.5819, 0.2525) X_40 = BEVAN POINT (0.4286, -0.0292) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_894 = ISOGONAL CONJUGATE OF X(893) (0.5501, 0.2184) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_986 = INTERSECTION OF LINES X(1)X(3) AND X(8)X(38) (0.5588, 0.2101) X_1046 = -CEVA CONJUGATE OF X(1) (0.6500, 0.3366) A B C X65 X1 X21 X43 X46 X72 X171 X40 X511 X10 X894 X6 X986 X1046 (a, b, c) = (5, 6, 7) | AB = 1

X1046 (X65-CEVA CONJUGATE OF X1) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(-u^{2} + v^{2} + w^{2} + vw + wu + uv\), where \(u : v : w\) = X3
Search Value (6, 9, 13): \(-0.186444018733\)
▸ Linear Combinations1 combination
▸ Incident Central Lines10 lines

{1, 21}, {4, 2648}, {6, 986}, {10, 894}, {40, 511}, {43, 46}, {57, 978}, {72, 171}, {238, 942}, {484, 1048}

▸ Functional Relations5 relations

Notes

Let La be the line parallel to the Brocard axis of BCI and passing through the A-excenter. Define Lb and Lc cyclically. The lines La, Lb, Lc concur in X1046. (Randy Hutson, January 29, 2018)