X1349
EXSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE)
X1349 is the exsimilicenter(nine-point circle, Brocard circle).
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) { 5, 182 }: Central Line L(5, 182) { 2, 1340 }: Central Line L(2, 1340) { 4, 1341 }: Central Line L(4, 1341)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5500, 0.1846) X_2 = CENTROID (0.5374, 0.2000) X_1340 = INSIMILICENTER(CIRCUMCIRCLE, BROCARD CIRCLE) (0.5420, 0.1715) X_4 = ORTHOCENTER (0.6122, 0.3958) X_1341 = EXSIMILICENTER(CIRCUMCIRCLE, BROCARD CIRCLE) (0.5617, 0.2039) X_1349 = EXSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE) (0.5463, 0.1455)
A
B
C
X5
X182
X2
X1340
X4
X1341
X1349
(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) { 5, 182 }: Central Line L(5, 182) { 2, 1340 }: Central Line L(2, 1340) { 4, 1341 }: Central Line L(4, 1341)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_5 = NINE-POINT CENTER (0.5700, 0.2400) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5700, 0.1200) X_2 = CENTROID (0.5467, 0.1600) X_1340 = INSIMILICENTER(CIRCUMCIRCLE, BROCARD CIRCLE) (0.5548, 0.0939) X_4 = ORTHOCENTER (0.6400, 0.4800) X_1341 = EXSIMILICENTER(CIRCUMCIRCLE, BROCARD CIRCLE) (0.5969, 0.1662) X_1349 = EXSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE) (0.5700, -0.0301)
A
B
C
X5
X182
X2
X1340
X4
X1341
X1349
(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) { 5, 182 }: Central Line L(5, 182) { 2, 1340 }: Central Line L(2, 1340) { 4, 1341 }: Central Line L(4, 1341)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_5 = NINE-POINT CENTER (0.5590, 0.2429) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5590, 0.1215) X_2 = CENTROID (0.5393, 0.1620) X_1340 = INSIMILICENTER(CIRCUMCIRCLE, BROCARD CIRCLE) (0.5465, 0.0956) X_4 = ORTHOCENTER (0.6180, 0.4859) X_1341 = EXSIMILICENTER(CIRCUMCIRCLE, BROCARD CIRCLE) (0.5809, 0.1664) X_1349 = EXSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE) (0.5590, -0.0212)
A
B
C
X5
X182
X2
X1340
X4
X1341
X1349
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) { 5, 182 }: Central Line L(5, 182) { 2, 1340 }: Central Line L(2, 1340) { 4, 1341 }: Central Line L(4, 1341)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_5 = NINE-POINT CENTER (0.5666, 0.2774) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5787, -0.0546) X_2 = CENTROID (0.5444, 0.0934) X_1340 = INSIMILICENTER(CIRCUMCIRCLE, BROCARD CIRCLE) (0.5558, -0.1186) X_4 = ORTHOCENTER (0.6331, 0.8294) X_1341 = EXSIMILICENTER(CIRCUMCIRCLE, BROCARD CIRCLE) (0.6333, 0.0981) X_1349 = EXSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE) (0.6336, -1.5605)
A
B
C
X5
X182
X2
X1340
X4
X1341
X1349
Kimberling (6, 9, 13) | AB = 1
X1349 (EXSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE) ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \(e \cos(B - C) - \cos(A - \omega )\) , where \(e = (1 - 4 \sin^{2}\omega )^{1/2}\)
Search Value (6, 9, 13): \(19.015368878919\)
▸ Alternate Coordinates1 form
▸ Linear Combinations1 combination
▸ Incident Central Lines3 lines
{2 1340 4 1341 5 182
▸ Functional Relations1 relation
