X147
TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE
X147 is the {
X98 ,
X114 }-harmonic conjugate of
X2 . For a list of harmonic conjugates, click
Tables at the top of this page.
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) { 98, 114 }: Central Line L(98, 114) { 2, 98 }: Central Line L(2, 98) { 20, 99 }: Central Line L(20, 99) { 1, 150 }: Central Line L(1, 150) { 4, 148 }: Central Line L(4, 148)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_98 = TARRY POINT (0.8891, -0.2281) X_114 = KIEPERT ANTIPODE (0.3616, 0.4140) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_99 = STEINER POINT (0.1109, 0.4322) X_1 = INCENTER (0.5714, 0.2333) X_150 = REFLECTION OF X(20) IN X(103) (1.1837, -0.4499) X_4 = ORTHOCENTER (0.6122, 0.3958) X_148 = STEINER POINT OF ANTICOMPLEMENTARY TRIANGLE (1.3904, -0.2646) X_147 = TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE (-0.1660, 1.0561)
A
B
C
X2
X98
X114
X20
X99
X1
X150
X4
X148
X147
(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) { 98, 114 }: Central Line L(98, 114) { 2, 98 }: Central Line L(2, 98) { 20, 99 }: Central Line L(20, 99) { 1, 150 }: Central Line L(1, 150) { 4, 148 }: Central Line L(4, 148)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_2 = CENTROID (0.5467, 0.1600) X_98 = TARRY POINT (0.8489, -0.3581) X_114 = KIEPERT ANTIPODE (0.3955, 0.4191) X_20 = DE LONGCHAMPS POINT (0.3600, -0.4800) X_99 = STEINER POINT (0.1511, 0.3581) X_1 = INCENTER (0.6000, 0.2000) X_150 = REFLECTION OF X(20) IN X(103) (1.0246, -0.4431) X_4 = ORTHOCENTER (0.6400, 0.4800) X_148 = STEINER POINT OF ANTICOMPLEMENTARY TRIANGLE (1.3378, -0.2363) X_147 = TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE (-0.0578, 1.1963)
A
B
C
X2
X98
X114
X20
X99
X1
X150
X4
X148
X147
(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) { 98, 114 }: Central Line L(98, 114) { 2, 98 }: Central Line L(2, 98) { 20, 99 }: Central Line L(20, 99) { 1, 150 }: Central Line L(1, 150) { 4, 148 }: Central Line L(4, 148)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_2 = CENTROID (0.5393, 0.1620) X_98 = TARRY POINT (0.8090, -0.3931) X_114 = KIEPERT ANTIPODE (0.4045, 0.4395) X_20 = DE LONGCHAMPS POINT (0.3820, -0.4859) X_99 = STEINER POINT (0.1910, 0.3931) X_1 = INCENTER (0.5841, 0.2021) X_150 = REFLECTION OF X(20) IN X(103) (0.9450, -0.4592) X_4 = ORTHOCENTER (0.6180, 0.4859) X_148 = STEINER POINT OF ANTICOMPLEMENTARY TRIANGLE (1.2361, -0.3003) X_147 = TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE (0.0000, 1.2720)
A
B
C
X2
X98
X114
X20
X99
X1
X150
X4
X148
X147
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) { 98, 114 }: Central Line L(98, 114) { 2, 98 }: Central Line L(2, 98) { 20, 99 }: Central Line L(20, 99) { 1, 150 }: Central Line L(1, 150) { 4, 148 }: Central Line L(4, 148)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_2 = CENTROID (0.5444, 0.0934) X_98 = TARRY POINT (0.7487, -0.7881) X_114 = KIEPERT ANTIPODE (0.4422, 0.5341) X_20 = DE LONGCHAMPS POINT (0.3669, -1.3788) X_99 = STEINER POINT (0.2513, 0.2387) X_1 = INCENTER (0.6154, 0.1300) X_150 = REFLECTION OF X(20) IN X(103) (0.7368, -0.3068) X_4 = ORTHOCENTER (0.6331, 0.8294) X_148 = STEINER POINT OF ANTICOMPLEMENTARY TRIANGLE (1.1305, -0.1974) X_147 = TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE (0.1358, 1.8562)
A
B
C
X2
X98
X114
X20
X99
X1
X150
X4
X148
X147
Kimberling (6, 9, 13) | AB = 1
X147 (TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \(bc[a^{8} + (b^{2} + c^{2})a^{6} - (2b^{4} + 3b^{2}c^{2} + 2c^{4})a^{4} + (b^{6} + b^{4}c^{2} + b^{2}c^{4} + c^{6})a^{2} - b^{8} + b^{6}c^{2} + b^{2}c^{6} - c^{8}] : :\)
Barycentrics: \(a \sec(A + \omega ) - b \sec(B + \omega ) - c \sec(C + \omega ) : :\)
Search Value (6, 9, 13): \(-12.363886292023\)
X147
▸ Incident Central Lines7 lines
{1 150 2 98 4 148 20 99 132 648 146 690 684 804
▸ Functional Relations13 relations
Notes
Let T be the P -Brocard triangle for any P on the Brocard axis (including the 1st Brocard triangle , for P = X6 OA be the circle centered at the A -vertex of T and passing through A ; define OB and OC cyclically. X147 OA , OB , OC . (Randy Hutson , August 30, 2020)
