X2464
EXSIMILICENTER(ORTHOCENTROIDAL CIRCLE, INCIRCLE)
X2464 is the exsimilicenter(orthocentroidal circle, incircle).
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) { 1, 381 }: Central Line L(1, 381) { 56, 1345 }: Central Line L(56, 1345) { 2, 2467 }: Central Line L(2, 2467) { 8, 2468 }: Central Line L(8, 2468) { 388, 2552 }: Central Line L(388, 2552) { 497, 2553 }: Central Line L(497, 2553)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_381 = MIDPOINT OF X(2) AND X(4) (0.5748, 0.2979) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_1345 = EXSIMILICENTER(CIRCUMCIRCLE, ORTHOCENTROIDAL CIRCLE) (0.5942, 0.3485) X_2 = CENTROID (0.5374, 0.2000) X_2467 = INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, SPIEKER CIRCLE) (0.5491, 0.2436) X_8 = NAGEL POINT (0.4694, 0.1333) X_2468 = EXSIMILICENTER(ORTHOCENTROIDALCIRCLE, SPIEKER CIRCLE) (1.0566, 1.3119) X_388 = ∩X(7)X(8) (0.5790, 0.2635) X_2552 = INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, (X(4),2R)) (0.5783, 0.3070) X_497 = CROSSPOINT OF GERGONNE POINT AND NAGEL POINT (0.5593, 0.1851) X_2553 = EXSIMILICENTER(ORTHOCENTROIDAL CIRCLE, (X(4),2R)) (0.5705, 0.2867) X_2464 = EXSIMILICENTER(ORTHOCENTROIDAL CIRCLE, INCIRCLE) (0.5776, 0.3505)
A
B
C
X1
X381
X56
X1345
X2
X2467
X8
X2468
X388
X2552
X497
X2553
X2464
(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) { 1, 381 }: Central Line L(1, 381) { 56, 1345 }: Central Line L(56, 1345) { 2, 2467 }: Central Line L(2, 2467) { 8, 2468 }: Central Line L(8, 2468) { 388, 2552 }: Central Line L(388, 2552) { 497, 2553 }: Central Line L(497, 2553)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_1 = INCENTER (0.6000, 0.2000) X_381 = MIDPOINT OF X(2) AND X(4) (0.5933, 0.3200) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6667, 0.3333) X_1345 = EXSIMILICENTER(CIRCUMCIRCLE, ORTHOCENTROIDAL CIRCLE) (0.6400, 0.4800) X_2 = CENTROID (0.5467, 0.1600) X_2467 = INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, SPIEKER CIRCLE) (0.5475, 0.2075) X_8 = NAGEL POINT (0.4400, 0.0800) X_2468 = EXSIMILICENTER(ORTHOCENTROIDALCIRCLE, SPIEKER CIRCLE) (0.4100, -0.1300) X_388 = ∩X(7)X(8) (0.6067, 0.2467) X_2552 = INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, (X(4),2R)) (0.6000, 0.3429) X_497 = CROSSPOINT OF GERGONNE POINT AND NAGEL POINT (0.5900, 0.1300) X_2553 = EXSIMILICENTER(ORTHOCENTROIDAL CIRCLE, (X(4),2R)) (0.5840, 0.2880) X_2464 = EXSIMILICENTER(ORTHOCENTROIDAL CIRCLE, INCIRCLE) (0.5600, 0.9200)
A
B
C
X1
X381
X56
X1345
X2
X2467
X8
X2468
X388
X2552
X497
X2553
X2464
(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) { 1, 381 }: Central Line L(1, 381) { 56, 1345 }: Central Line L(56, 1345) { 2, 2467 }: Central Line L(2, 2467) { 8, 2468 }: Central Line L(8, 2468) { 388, 2552 }: Central Line L(388, 2552) { 497, 2553 }: Central Line L(497, 2553)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_1 = INCENTER (0.5841, 0.2021) X_381 = MIDPOINT OF X(2) AND X(4) (0.5787, 0.3239) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6411, 0.3392) X_1345 = EXSIMILICENTER(CIRCUMCIRCLE, ORTHOCENTROIDAL CIRCLE) (0.6180, 0.4859) X_2 = CENTROID (0.5393, 0.1620) X_2467 = INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, SPIEKER CIRCLE) (0.5403, 0.2106) X_8 = NAGEL POINT (0.4499, 0.0817) X_2468 = EXSIMILICENTER(ORTHOCENTROIDALCIRCLE, SPIEKER CIRCLE) (0.4220, -0.1384) X_388 = ∩X(7)X(8) (0.5898, 0.2498) X_2552 = INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, (X(4),2R)) (0.5843, 0.3470) X_497 = CROSSPOINT OF GERGONNE POINT AND NAGEL POINT (0.5755, 0.1302) X_2553 = EXSIMILICENTER(ORTHOCENTROIDAL CIRCLE, (X(4),2R)) (0.5708, 0.2915) X_2464 = EXSIMILICENTER(ORTHOCENTROIDAL CIRCLE, INCIRCLE) (0.5534, 0.8970)
A
B
C
X1
X381
X56
X1345
X2
X2467
X8
X2468
X388
X2552
X497
X2553
X2464
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) { 1, 381 }: Central Line L(1, 381) { 56, 1345 }: Central Line L(56, 1345) { 2, 2467 }: Central Line L(2, 2467) { 8, 2468 }: Central Line L(8, 2468) { 388, 2552 }: Central Line L(388, 2552) { 497, 2553 }: Central Line L(497, 2553)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_1 = INCENTER (0.6154, 0.1300) X_381 = MIDPOINT OF X(2) AND X(4) (0.5888, 0.4614) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6494, 0.2495) X_1345 = EXSIMILICENTER(CIRCUMCIRCLE, ORTHOCENTROIDAL CIRCLE) (0.7534, 1.8271) X_2 = CENTROID (0.5444, 0.0934) X_2467 = INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, SPIEKER CIRCLE) (0.5208, 0.1327) X_8 = NAGEL POINT (0.4024, 0.0200) X_2468 = EXSIMILICENTER(ORTHOCENTROIDALCIRCLE, SPIEKER CIRCLE) (0.4919, -0.0072) X_388 = ∩X(7)X(8) (0.6172, 0.2016) X_2552 = INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, (X(4),2R)) (0.5996, 0.5516) X_497 = CROSSPOINT OF GERGONNE POINT AND NAGEL POINT (0.6131, 0.0401) X_2553 = EXSIMILICENTER(ORTHOCENTROIDAL CIRCLE, (X(4),2R)) (0.5674, 0.2843) X_2464 = EXSIMILICENTER(ORTHOCENTROIDAL CIRCLE, INCIRCLE) (0.6298, -0.0490)
A
B
C
X1
X381
X56
X1345
X2
X2467
X8
X2468
X388
X2552
X497
X2553
X2464
Kimberling (6, 9, 13) | AB = 1
X2464 (EXSIMILICENTER(ORTHOCENTROIDAL CIRCLE, INCIRCLE) ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\) , where
\(f(A,B,C) = J - \cos A - 4 \cos B \cos C\) , J as at
X1113 Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(3.426675401643\)
▸ Linear Combinations1 combination
▸ Incident Central Lines12 lines
{1 381 2 2467 8 2468 56 1345 388 2552 497 2553 1124 2465 1335 2466 1672 2471 1673 2472 1634 2469 1675 2470
