X1486
PERSPECTOR OF TANGENTIAL AND INTOUCH TRIANGLES
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) { 19, 25 }: Central Line L(19, 25) { 3, 142 }: Central Line L(3, 142) { 1, 159 }: Central Line L(1, 159) { 100, 344 }: Central Line L(100, 344) { 6, 692 }: Central Line L(6, 692) { 219, 674 }: Central Line L(219, 674)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_19 = CLAWSON POINT (0.6246, 0.4244) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_142 = COMPLEMENT OF X(9) (0.5506, 0.2192) X_1 = INCENTER (0.5714, 0.2333) X_159 = -OF-TANGENTIAL-TRIANGLE (0.4211, -0.7266) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_344 = ISOTOMIC CONJUGATE OF X(277) (0.6218, 0.2693) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_692 = -CEVA CONJUGATE OF X(101) (0.2833, 0.5715) X_219 = -CEVA CONJUGATE OF X(55) (0.4277, 0.0625) X_674 = CROSSDIFFERENCE OF X(6) AND X(514) (0.2078, -0.2856) X_1486 = PERSPECTOR OF TANGENTIAL AND INTOUCH TRIANGLES (0.5798, 0.2866)
A
B
C
X19
X25
X3
X142
X1
X159
X100
X344
X6
X692
X219
X674
X1486
(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) { 3, 142 }: Central Line L(3, 142) { 1, 159 }: Central Line L(1, 159) { 100, 344 }: Central Line L(100, 344) { 6, 692 }: Central Line L(6, 692) { 219, 674 }: Central Line L(219, 674) { 56, 1279 }: Central Line L(56, 1279)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_3 = CIRCUMCENTER (0.5000, 0.0000) X_142 = COMPLEMENT OF X(9) (0.5655, 0.1855) X_1 = INCENTER (0.6000, 0.2000) X_159 = -OF-TANGENTIAL-TRIANGLE (0.5467, -0.4150) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.2000, 0.4000) X_344 = ISOTOMIC CONJUGATE OF X(277) (0.7053, 0.2526) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6400, 0.2400) X_692 = -CEVA CONJUGATE OF X(101) (0.4000, 0.5000) X_219 = -CEVA CONJUGATE OF X(55) (0.4000, 0.0000) X_674 = CROSSDIFFERENCE OF X(6) AND X(514) (0.2151, -0.3098) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6667, 0.3333) X_1279 = MIDPOINT OF X(1) AND X(238) (0.9333, 0.5333) X_1486 = PERSPECTOR OF TANGENTIAL AND INTOUCH TRIANGLES (0.6000, 0.2833)
A
B
C
X3
X142
X1
X159
X100
X344
X6
X692
X219
X674
X56
X1279
X1486
(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) { 3, 142 }: Central Line L(3, 142) { 1, 159 }: Central Line L(1, 159) { 100, 344 }: Central Line L(100, 344) { 6, 692 }: Central Line L(6, 692) { 219, 674 }: Central Line L(219, 674) { 56, 1279 }: Central Line L(56, 1279)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_3 = CIRCUMCENTER (0.5000, 0.0000) X_142 = COMPLEMENT OF X(9) (0.5552, 0.1878) X_1 = INCENTER (0.5841, 0.2021) X_159 = -OF-TANGENTIAL-TRIANGLE (0.5393, -0.4130) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.2386, 0.4263) X_344 = ISOTOMIC CONJUGATE OF X(277) (0.6689, 0.2517) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6180, 0.2429) X_692 = -CEVA CONJUGATE OF X(101) (0.4159, 0.5000) X_219 = -CEVA CONJUGATE OF X(55) (0.4159, 0.0000) X_674 = CROSSDIFFERENCE OF X(6) AND X(514) (0.2481, -0.3338) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6411, 0.3392) X_1279 = MIDPOINT OF X(1) AND X(238) (0.8931, 0.5736) X_1486 = PERSPECTOR OF TANGENTIAL AND INTOUCH TRIANGLES (0.5841, 0.2862)
A
B
C
X3
X142
X1
X159
X100
X344
X6
X692
X219
X674
X56
X1279
X1486
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) { 19, 25 }: Central Line L(19, 25) { 3, 142 }: Central Line L(3, 142) { 1, 159 }: Central Line L(1, 159) { 100, 344 }: Central Line L(100, 344) { 6, 692 }: Central Line L(6, 692) { 219, 674 }: Central Line L(219, 674)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_19 = CLAWSON POINT (0.5737, 0.4687) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.5783, 0.3748) X_3 = CIRCUMCENTER (0.5000, -0.2747) X_142 = COMPLEMENT OF X(9) (0.5655, 0.1229) X_1 = INCENTER (0.6154, 0.1300) X_159 = -OF-TANGENTIAL-TRIANGLE (0.4654, 0.6738) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.3206, 0.2669) X_344 = ISOTOMIC CONJUGATE OF X(277) (0.8829, 0.2111) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6573, 0.1655) X_692 = -CEVA CONJUGATE OF X(101) (0.5270, 0.3006) X_219 = -CEVA CONJUGATE OF X(55) (0.4333, -0.0239) X_674 = CROSSDIFFERENCE OF X(6) AND X(514) (0.2182, -0.4758) X_1486 = PERSPECTOR OF TANGENTIAL AND INTOUCH TRIANGLES (0.5849, 0.2406)
A
B
C
X19
X25
X3
X142
X1
X159
X100
X344
X6
X692
X219
X674
X1486
Kimberling (6, 9, 13) | AB = 1
X1486 (PERSPECTOR OF TANGENTIAL AND INTOUCH TRIANGLES ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \(a[ - a^{2}(b + c - a) + b^{2}(c + a - b) + c^{2}(a + b - c)] : :\)
Search Value (6, 9, 13): \(0.788014663339\)
▸ Incident Central Lines9 lines
{1 159 3 142 6 692 19 25 56 1279 100 344 219 674 354 1473 513 1037
▸ Functional Relations8 relations
Notes
Let Ta Tb Tc be the intouch triangle. Let A″ be the crosspoint of the circumcircle intercepts of line Tb Tc , and define B″ and C″ cyclically. The lines Ta A″ , Tb B″ , Tc C″ concur in X1486
