X1274
ISOTOMIC CONJUGATE OF X1143
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) { 8, 177 }: Central Line L(8, 177) { 174, 176 }: Central Line L(174, 176) { 2, 1489 }: Central Line L(2, 1489) { 557, 1488 }: Central Line L(557, 1488)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1143 = 2nd MALFATTI-RABINOWITZ POINT (0.5857, 0.2649) X_8 = NAGEL POINT (0.4694, 0.1333) X_177 = 1st MID-ARC POINT (0.5862, 0.2654) X_174 = YFF CENTER OF CONGRUENCE (0.5813, 0.2549) X_176 = EQUAL DETOUR POINT (0.5803, 0.2537) X_2 = CENTROID (0.5374, 0.2000) X_1489 = 3rd STEVANOVIC POINT (0.5675, 0.2288) X_557 = (X(1),X(9))-ANSWER TO QUESTION A (0.5314, 0.1908) X_1488 = 2nd STEVANOVIC POINT (0.5582, 0.2148) X_1274 = ISOTOMIC CONJUGATE OF X(1143) (0.4773, 0.1423)
A
B
C
X1143
X8
X177
X174
X176
X2
X1489
X557
X1488
X1274
(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) { 8, 177 }: Central Line L(8, 177) { 174, 176 }: Central Line L(174, 176) { 2, 1489 }: Central Line L(2, 1489) { 557, 1488 }: Central Line L(557, 1488)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_1143 = 2nd MALFATTI-RABINOWITZ POINT (0.6168, 0.2447) X_8 = NAGEL POINT (0.4400, 0.0800) X_177 = 1st MID-ARC POINT (0.6174, 0.2453) X_174 = YFF CENTER OF CONGRUENCE (0.6119, 0.2308) X_176 = EQUAL DETOUR POINT (0.6104, 0.2296) X_2 = CENTROID (0.5467, 0.1600) X_1489 = 3rd STEVANOVIC POINT (0.5944, 0.1948) X_557 = (X(1),X(9))-ANSWER TO QUESTION A (0.5382, 0.1476) X_1488 = 2nd STEVANOVIC POINT (0.5818, 0.1764) X_1274 = ISOTOMIC CONJUGATE OF X(1143) (0.4512, 0.0904)
A
B
C
X1143
X8
X177
X174
X176
X2
X1489
X557
X1488
X1274
(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) { 8, 177 }: Central Line L(8, 177) { 174, 176 }: Central Line L(174, 176) { 2, 1489 }: Central Line L(2, 1489) { 557, 1488 }: Central Line L(557, 1488)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_1143 = 2nd MALFATTI-RABINOWITZ POINT (0.5983, 0.2477) X_8 = NAGEL POINT (0.4499, 0.0817) X_177 = 1st MID-ARC POINT (0.5989, 0.2484) X_174 = YFF CENTER OF CONGRUENCE (0.5941, 0.2335) X_176 = EQUAL DETOUR POINT (0.5929, 0.2323) X_2 = CENTROID (0.5393, 0.1620) X_1489 = 3rd STEVANOVIC POINT (0.5793, 0.1968) X_557 = (X(1),X(9))-ANSWER TO QUESTION A (0.5322, 0.1494) X_1488 = 2nd STEVANOVIC POINT (0.5687, 0.1780) X_1274 = ISOTOMIC CONJUGATE OF X(1143) (0.4594, 0.0923)
A
B
C
X1143
X8
X177
X174
X176
X2
X1489
X557
X1488
X1274
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) { 8, 177 }: Central Line L(8, 177) { 174, 176 }: Central Line L(174, 176) { 2, 1489 }: Central Line L(2, 1489) { 557, 1488 }: Central Line L(557, 1488)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_1143 = 2nd MALFATTI-RABINOWITZ POINT (0.6262, 0.1903) X_8 = NAGEL POINT (0.4024, 0.0200) X_177 = 1st MID-ARC POINT (0.6266, 0.1906) X_174 = YFF CENTER OF CONGRUENCE (0.6235, 0.1737) X_176 = EQUAL DETOUR POINT (0.6225, 0.1730) X_2 = CENTROID (0.5444, 0.0934) X_1489 = 3rd STEVANOVIC POINT (0.6100, 0.1259) X_557 = (X(1),X(9))-ANSWER TO QUESTION A (0.5341, 0.0778) X_1488 = 2nd STEVANOVIC POINT (0.5987, 0.1042) X_1274 = ISOTOMIC CONJUGATE OF X(1143) (0.4132, 0.0282)
A
B
C
X1143
X8
X177
X174
X176
X2
X1489
X557
X1488
X1274
Kimberling (6, 9, 13) | AB = 1
X1274 (ISOTOMIC CONJUGATE OF X1143 ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \(1/(a^{2}f(a,b,c)) : 1/(b^{2}f(b,c,a)) : 1/(c^{2}f(c,a,b))\) , where f(a,b,c) is as in
X1143 )
Search Value (6, 9, 13): \(4.337495525746\)
▸ Alternate Coordinates1 form
Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\) , where \(g(A, B, C) = (\csc A)(\cot A/4)\)
X1274
▸ Incident Central Lines4 lines
{2 1489 8 177 174 176 557 1488
▸ Functional Relations2 relations
Notes
Let I be the incenter of ABC and EA the excircle of triangle BCI that touches segment BC , and let A' be the touchpoint. Define B' and C' cyclically. The lines AA' , BB' , CC' concur in X1274 Randy Hutson , 9/23/2011)
