X1255
ISOGONAL CONJUGATE OF X1100
5, 6, 7
3, 4, 5
Kepler
Kimberling
< 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) { 37, 81 }: Central Line L(37, 81) { 274, 321 }: Central Line L(274, 321) { 2, 594 }: Central Line L(2, 594) { 278, 469 }: Central Line L(278, 469) { 1, 748 }: Central Line L(1, 748) { 89, 940 }: Central Line L(89, 940)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1100 = COMPLEMENT OF X(319) (0.5787, 0.2419) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_274 = ISOGONAL CONJUGATE OF X(213) (0.5168, 0.1843) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_2 = CENTROID (0.5374, 0.2000) X_594 = ISOGONAL CONJUGATE OF X(593) (0.5025, 0.1672) X_278 = ISOGONAL CONJUGATE OF X(219) (0.6278, 0.4577) X_469 = EULER LINE INTERCEPT OF LINE X(92)X(264) (0.6071, 0.3824) X_1 = INCENTER (0.5714, 0.2333) X_748 = INTERSECTION OF LINES X(2)X(31) AND X(9)X(38) (0.4360, 0.0802) X_89 = ISOGONAL CONJUGATE OF X(45) (0.5963, 0.2697) X_940 = POINT ALDEBARAN (0.5757, 0.2411) X_1255 = ISOGONAL CONJUGATE OF X(1100) (0.5639, 0.2247)
A
B
C
X1100
X37
X81
X274
X321
X2
X594
X278
X469
X1
X748
X89
X940
X1255
(a, b, c) = (5, 6, 7) | AB = 1
< 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) { 37, 81 }: Central Line L(37, 81) { 274, 321 }: Central Line L(274, 321) { 2, 594 }: Central Line L(2, 594) { 1, 748 }: Central Line L(1, 748) { 89, 940 }: Central Line L(89, 940) { 1125, 1224 }: Central Line L(1125, 1224)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_1100 = COMPLEMENT OF X(319) (0.6103, 0.2103) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5787, 0.1787) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.6185, 0.2215) X_274 = ISOGONAL CONJUGATE OF X(213) (0.5114, 0.1416) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4525, 0.1050) X_2 = CENTROID (0.5467, 0.1600) X_594 = ISOGONAL CONJUGATE OF X(593) (0.4915, 0.1212) X_1 = INCENTER (0.6000, 0.2000) X_748 = INTERSECTION OF LINES X(2)X(31) AND X(9)X(38) (0.3667, -0.0167) X_89 = ISOGONAL CONJUGATE OF X(45) (0.6327, 0.2449) X_940 = POINT ALDEBARAN (0.6050, 0.2100) X_1125 = COMPLEMENT OF X(10) (0.5600, 0.1700) X_1224 = ISOGONAL CONJUGATE OF X(1203) (0.5387, 0.1555) X_1255 = ISOGONAL CONJUGATE OF X(1100) (0.5889, 0.1897)
A
B
C
X1100
X37
X81
X274
X321
X2
X594
X1
X748
X89
X940
X1125
X1224
X1255
(a, b, c) = (3, 4, 5) | AB = 1
< 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) { 37, 81 }: Central Line L(37, 81) { 274, 321 }: Central Line L(274, 321) { 2, 594 }: Central Line L(2, 594) { 1, 748 }: Central Line L(1, 748) { 89, 940 }: Central Line L(89, 940) { 1125, 1224 }: Central Line L(1125, 1224)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_1100 = COMPLEMENT OF X(319) (0.5928, 0.2126) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5661, 0.1805) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5997, 0.2241) X_274 = ISOGONAL CONJUGATE OF X(213) (0.5101, 0.1439) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4606, 0.1074) X_2 = CENTROID (0.5393, 0.1620) X_594 = ISOGONAL CONJUGATE OF X(593) (0.4931, 0.1231) X_1 = INCENTER (0.5841, 0.2021) X_748 = INTERSECTION OF LINES X(2)X(31) AND X(9)X(38) (0.3925, -0.0115) X_89 = ISOGONAL CONJUGATE OF X(45) (0.6118, 0.2481) X_940 = POINT ALDEBARAN (0.5883, 0.2124) X_1125 = COMPLEMENT OF X(10) (0.5505, 0.1720) X_1224 = ISOGONAL CONJUGATE OF X(1203) (0.5327, 0.1575) X_1255 = ISOGONAL CONJUGATE OF X(1100) (0.5747, 0.1917)
A
B
C
X1100
X37
X81
X274
X321
X2
X594
X1
X748
X89
X940
X1125
X1224
X1255
Kepler (1, √φ, φ) | AB = 1
< 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) { 37, 81 }: Central Line L(37, 81) { 274, 321 }: Central Line L(274, 321) { 2, 594 }: Central Line L(2, 594) { 278, 469 }: Central Line L(278, 469) { 1, 748 }: Central Line L(1, 748) { 89, 940 }: Central Line L(89, 940)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_1100 = COMPLEMENT OF X(319) (0.6266, 0.1395) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5913, 0.1097) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.6338, 0.1505) X_274 = ISOGONAL CONJUGATE OF X(213) (0.4902, 0.0774) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4100, 0.0466) X_2 = CENTROID (0.5444, 0.0934) X_594 = ISOGONAL CONJUGATE OF X(593) (0.4705, 0.0589) X_278 = ISOGONAL CONJUGATE OF X(219) (0.6201, 0.3162) X_469 = EULER LINE INTERCEPT OF LINE X(92)X(264) (0.7605, 1.8855) X_1 = INCENTER (0.6154, 0.1300) X_748 = INTERSECTION OF LINES X(2)X(31) AND X(9)X(38) (0.1616, -0.2076) X_89 = ISOGONAL CONJUGATE OF X(45) (0.6444, 0.1737) X_940 = POINT ALDEBARAN (0.6184, 0.1406) X_1255 = ISOGONAL CONJUGATE OF X(1100) (0.6026, 0.1205)
A
B
C
X1100
X37
X81
X274
X321
X2
X594
X278
X469
X1
X748
X89
X940
X1255
Kimberling (6, 9, 13) | AB = 1
X1255 (ISOGONAL CONJUGATE OF X1100 ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \(1/f(a,b,c) : 1/f(b,c,a) : 1/f(c,a,b)\) , where f(a,b,c) is as in
X1100 )
Search Value (6, 9, 13): \(1.889309621801\)
▸ Incident Central Lines7 lines
{1 748 2 594 37 81 89 940 274 321 278 469 1125 1224
▸ Functional Relations7 relations
Notes
Let A12 B12 C12 be Gemini triangle 12. Let A' be the perspector of conic {{A , B , C ,B12 ,C12 }}, and define B' and C' cyclically. The lines AA' , BB' , CC' concur in X1255 Randy Hutson , January 15, 2019)
