X897
ISOGONAL CONJUGATE OF X896
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) { 37, 100 }: Central Line L(37, 100) { 19, 162 }: Central Line L(19, 162) { 10, 190 }: Central Line L(10, 190) { 1, 662 }: Central Line L(1, 662) { 65, 651 }: Central Line L(65, 651) { 75, 799 }: Central Line L(75, 799)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_896 = INTERSECTION OF LINES X(1)X(21) AND X(9)X(750) (2.0357, 2.1579) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_19 = CLAWSON POINT (0.6246, 0.4244) X_162 = CEVAPOINT OF X(108) AND X(109) (0.4897, 0.6018) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_1 = INCENTER (0.5714, 0.2333) X_662 = TRILINEAR POLE OF LINE X(1)X(21) (0.1811, 0.4951) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.3048, 0.5599) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_799 = ISOGONAL CONJUGATE OF X(798) (0.0470, 0.3636) X_897 = ISOGONAL CONJUGATE OF X(896) (0.9765, -0.0384)
A
B
C
X896
X37
X100
X19
X162
X10
X190
X1
X662
X65
X651
X75
X799
X897
(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) { 37, 100 }: Central Line L(37, 100) { 10, 190 }: Central Line L(10, 190) { 1, 662 }: Central Line L(1, 662) { 65, 651 }: Central Line L(65, 651) { 75, 799 }: Central Line L(75, 799) { 691, 759 }: Central Line L(691, 759)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_896 = INTERSECTION OF LINES X(1)X(21) AND X(9)X(750) (1.5000, 1.2500) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5787, 0.1787) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.2000, 0.4000) X_10 = SPIEKER CENTER (0.5200, 0.1400) X_190 = YFF PARABOLIC POINT (0.0933, 0.3200) X_1 = INCENTER (0.6000, 0.2000) X_662 = TRILINEAR POLE OF LINE X(1)X(21) (0.2597, 0.4299) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6400, 0.2800) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.4400, 0.4800) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4826, 0.1226) X_799 = ISOGONAL CONJUGATE OF X(798) (0.0532, 0.2744) X_691 = TRILINEAR POLE OF LINE X(6)X(110) (0.9867, 0.1144) X_759 = EVEN (1, 3) CIRCUMCIRCLE POINT (0.9529, -0.2118) X_897 = ISOGONAL CONJUGATE OF X(896) (0.9697, -0.0497)
A
B
C
X896
X37
X100
X10
X190
X1
X662
X65
X651
X75
X799
X691
X759
X897
(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) { 37, 100 }: Central Line L(37, 100) { 10, 190 }: Central Line L(10, 190) { 1, 662 }: Central Line L(1, 662) { 65, 651 }: Central Line L(65, 651) { 75, 799 }: Central Line L(75, 799) { 691, 759 }: Central Line L(691, 759)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_896 = INTERSECTION OF LINES X(1)X(21) AND X(9)X(750) (1.4082, 1.3593) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5661, 0.1805) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.2386, 0.4263) X_10 = SPIEKER CENTER (0.5170, 0.1419) X_190 = YFF PARABOLIC POINT (0.1322, 0.3610) X_1 = INCENTER (0.5841, 0.2021) X_662 = TRILINEAR POLE OF LINE X(1)X(21) (0.2938, 0.4492) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6180, 0.2838) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.4499, 0.4859) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4859, 0.1249) X_799 = ISOGONAL CONJUGATE OF X(798) (0.0873, 0.3209) X_691 = TRILINEAR POLE OF LINE X(6)X(110) (0.9549, 0.2075) X_759 = EVEN (1, 3) CIRCUMCIRCLE POINT (0.9206, -0.2704) X_897 = ISOGONAL CONJUGATE OF X(896) (0.9332, -0.0950)
A
B
C
X896
X37
X100
X10
X190
X1
X662
X65
X651
X75
X799
X691
X759
X897
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) { 37, 100 }: Central Line L(37, 100) { 19, 162 }: Central Line L(19, 162) { 10, 190 }: Central Line L(10, 190) { 1, 662 }: Central Line L(1, 662) { 65, 651 }: Central Line L(65, 651) { 75, 799 }: Central Line L(75, 799)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_896 = INTERSECTION OF LINES X(1)X(21) AND X(9)X(750) (1.0099, 0.5674) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5913, 0.1097) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.3206, 0.2669) X_19 = CLAWSON POINT (0.5737, 0.4687) X_162 = CEVAPOINT OF X(108) AND X(109) (0.7026, 0.2691) X_10 = SPIEKER CENTER (0.5089, 0.0750) X_190 = YFF PARABOLIC POINT (0.1548, 0.2119) X_1 = INCENTER (0.6154, 0.1300) X_662 = TRILINEAR POLE OF LINE X(1)X(21) (0.3982, 0.2796) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6417, 0.2223) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.5832, 0.2846) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4506, 0.0607) X_799 = ISOGONAL CONJUGATE OF X(798) (0.0892, 0.1730) X_897 = ISOGONAL CONJUGATE OF X(896) (0.9342, -0.0894)
A
B
C
X896
X37
X100
X19
X162
X10
X190
X1
X662
X65
X651
X75
X799
X897
Kimberling (6, 9, 13) | AB = 1
X897 (ISOGONAL CONJUGATE OF X896 ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \(1/(2a^{2} - b^{2} - c^{2}) : :\)
Search Value (6, 9, 13): \(1.443596535574\)
▸ Incident Central Lines9 lines
{1 662 10 190 19 162 37 100 65 651 75 799 158 823 225 653 691 759
▸ Functional Relations7 relations
Notes
Let A1 B1 C1 and A3 B3 C3 be the 1st and 3rd Parry triangles. Let A' be the trilinear product A1 *A3 , and define B' and C' cyclically. The lines AA' , BB' , CC' concur in X897 Randy Hutson , February 10, 2016)
Let A'B'C' and A″B″C″ be the 4th Brocard and 4th anti-Brocard triangles, resp. Let A* be the trilinear product A' *A″ , and define B* , C* cyclically. The lines AA* , BB* , CC* concur in X897
