X2498
RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, MOSES 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) { 2494, 2495 }: Central Line L(2494, 2495) { 513, 676 }: Central Line L(513, 676) { 512, 2030 }: Central Line L(512, 2030)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2494 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, 1st LEMOINE CIRCLE} (4.6935, -1.3106) X_2495 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, 2nd LEMOINE CIRCLE} (-2.6701, 2.6976) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_676 = CROSSDIFFERENCE OF X(3) AND X(101) (1.2449, 0.5665) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_2030 = RADICAL TRACE OF MOSES CIRCLE AND CIRCUMCIRCLE (0.8993, 0.7615) X_2498 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, MOSES CIRCLE} (1.0117, 0.6935)
A
B
C
X2494
X2495
X513
X676
X512
X2030
X2498
(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) { 2494, 2495 }: Central Line L(2494, 2495) { 513, 676 }: Central Line L(513, 676) { 512, 2030 }: Central Line L(512, 2030)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_2494 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, 1st LEMOINE CIRCLE} (2.3200, -0.2600) X_2495 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, 2nd LEMOINE CIRCLE} (-0.5600, 1.1800) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0610, -0.0971) X_676 = CROSSDIFFERENCE OF X(3) AND X(101) (1.1200, 0.3400) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0433, -0.1297) X_2030 = RADICAL TRACE OF MOSES CIRCLE AND CIRCUMCIRCLE (0.7967, 0.5086) X_2498 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, MOSES CIRCLE} (0.8800, 0.4600)
A
B
C
X2494
X2495
X513
X676
X512
X2030
X2498
(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) { 2494, 2495 }: Central Line L(2494, 2495) { 513, 676 }: Central Line L(513, 676) { 512, 2030 }: Central Line L(512, 2030)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_2494 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, 1st LEMOINE CIRCLE} (2.6471, -0.2571) X_2495 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, 2nd LEMOINE CIRCLE} (-0.8270, 1.1880) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0703, -0.0589) X_676 = CROSSDIFFERENCE OF X(3) AND X(101) (1.2021, 0.3440) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0565, -0.0893) X_2030 = RADICAL TRACE OF MOSES CIRCLE AND CIRCUMCIRCLE (0.7613, 0.5377) X_2498 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, MOSES CIRCLE} (0.9101, 0.4654)
A
B
C
X2494
X2495
X513
X676
X512
X2030
X2498
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) { 2494, 2495 }: Central Line L(2494, 2495) { 513, 676 }: Central Line L(513, 676) { 512, 2030 }: Central Line L(512, 2030)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_2494 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, 1st LEMOINE CIRCLE} (1.3071, 0.0952) X_2495 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, 2nd LEMOINE CIRCLE} (0.1877, 0.4144) X_513 = ISOGONAL CONJUGATE OF X(100) (1.1753, -0.0865) X_676 = CROSSDIFFERENCE OF X(3) AND X(101) (1.1010, 0.1540) X_512 = ISOGONAL CONJUGATE OF X(99) (1.1621, -0.1275) X_2030 = RADICAL TRACE OF MOSES CIRCLE AND CIRCUMCIRCLE (0.6959, 0.2732) X_2498 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, MOSES CIRCLE} (0.7474, 0.2548)
A
B
C
X2494
X2495
X513
X676
X512
X2030
X2498
Kimberling (6, 9, 13) | AB = 1
X2498 (RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, MOSES CIRCLE} ) 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 \(f(a,b,c) = a[b^{2}(2a^{2} + 2b^{2} - c^{2})(a + c - b)^{2} - c^{2}(2a^{2} + 2c^{2} - b^{2})(a + b - c)^{2}]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.640049479623\)
▸ Incident Central Lines2 lines
▸ Functional Relations1 relation
