X2197

X2-ISOCONJUGATE OF X270

X2197 = X60-isoconjugate of X92
< 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) { 12, 37 }: Central Line L(12, 37) { 71, 73 }: Central Line L(71, 73) { 42, 181 }: Central Line L(42, 181) { 48, 216 }: Central Line L(48, 216) { 306, 307 }: Central Line L(306, 307) { 39, 604 }: Central Line L(39, 604) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_71 = ISOGONAL CONJUGATE OF X(27) (0.4807, 0.0915) X_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_181 = APOLLONIUS POINT (0.6163, 0.3093) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_216 = -CEVA CONJUGATE OF X(51) (0.5201, 0.1353) X_306 = ISOTOMIC CONJUGATE OF X(27) (0.3924, 0.0579) X_307 = ISOTOMIC CONJUGATE OF X(29) (0.4659, 0.0959) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_604 = -CEVA CONJUGATE OF X(31) (0.6442, 0.3744) X_2197 = -ISOCONJUGATE OF X(270) (0.5312, 0.1296) A B C X12 X37 X71 X73 X42 X181 X48 X216 X306 X307 X39 X604 X2197 (a, b, c) = (5, 6, 7) | AB = 1

X2197 (X2-ISOCONJUGATE OF X270) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(Trilinears (\sin 2A) (1 + \cos(B - C)) : :\)
Search Value (6, 9, 13): \(-4.677401199451\)
▸ Incident Central Lines19 lines

{3, 2286}, {6, 2259}, {9, 1937}, {12, 37}, {35, 1950}, {39, 604}, {41, 800}, {42, 181}, {48, 216}, {55, 608}, {71, 73}, {198, 607}, {222, 1796}, {278, 2335}, {306, 307}, {1030, 1415}, {1253, 2199}, {1254, 1500}, {2276, 2285}

▸ Functional Relations6 relations

Notes

Let IaIbIc be the cevian triangle of I (incenter) and let A″ be the intersection of the perpendicular bisector of AIa and the line through Ia perpendicular line to BC; note that A″(lies on AX3). Define B″ and C″ cyclically. The finite fixed point of the affine transformation that carries ABC onto IaIbIc is X2197, and the finite fixed point of the affine transformation that carries IaIbIc onto A″B″C″ is X2269. (Angel Montesdeoca, December 7, 2021)