X3324
INCIRCLE TRANSFORM T(X822 )
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) { 12, 122 }: Central Line L(12, 122) { 56, 107 }: Central Line L(56, 107) { 55, 1294 }: Central Line L(55, 1294) { 65, 1363 }: Central Line L(65, 1363) { 133, 1838 }: Central Line L(133, 1838)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_122 = -OF-MEDIAL-TRIANGLE (0.5195, -0.0036) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_107 = Ψ(SYMMEDIAN POINT, ORTHOCENTER) (0.5733, 0.6071) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_1294 = COLLINGS TRANSFORM OF X(122) (0.4267, -0.4030) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_1363 = BRISSE TRANSFORM OF X(107) (0.6026, 0.0021) X_133 = INTERSECTION OF LINES X(4)X(74) AND X(5)X(122) (0.5928, 0.5014) X_1838 = ZOSMA TRANSFORM OF X(35) (0.6188, 0.4218) X_3324 = INCIRCLE TRANSFORM T(X(822)) (0.6050, 0.4641)
A
B
C
X12
X122
X56
X107
X55
X1294
X65
X1363
X133
X1838
X3324
(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) { 12, 122 }: Central Line L(12, 122) { 56, 107 }: Central Line L(56, 107) { 55, 1294 }: Central Line L(55, 1294) { 65, 1363 }: Central Line L(65, 1363)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5867, 0.2178) X_122 = -OF-MEDIAL-TRIANGLE (0.5000, 0.0000) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6667, 0.3333) X_107 = Ψ(SYMMEDIAN POINT, ORTHOCENTER) (0.6400, 0.4800) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5714, 0.1429) X_1294 = COLLINGS TRANSFORM OF X(122) (0.3600, -0.4800) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6400, 0.2800) X_1363 = BRISSE TRANSFORM OF X(107) (0.6000, 0.0000) X_3324 = INCIRCLE TRANSFORM T(X(822)) (0.6560, 0.3920)
A
B
C
X12
X122
X56
X107
X55
X1294
X65
X1363
X3324
(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) { 12, 122 }: Central Line L(12, 122) { 56, 107 }: Central Line L(56, 107) { 55, 1294 }: Central Line L(55, 1294) { 65, 1363 }: Central Line L(65, 1363)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5729, 0.2203) X_122 = -OF-MEDIAL-TRIANGLE (0.5000, 0.0000) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6411, 0.3392) X_107 = Ψ(SYMMEDIAN POINT, ORTHOCENTER) (0.6180, 0.4859) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5599, 0.1439) X_1294 = COLLINGS TRANSFORM OF X(122) (0.3820, -0.4859) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6180, 0.2838) X_1363 = BRISSE TRANSFORM OF X(107) (0.5841, 0.0000) X_3324 = INCIRCLE TRANSFORM T(X(822)) (0.6318, 0.3985)
A
B
C
X12
X122
X56
X107
X55
X1294
X65
X1363
X3324
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) { 12, 122 }: Central Line L(12, 122) { 56, 107 }: Central Line L(56, 107) { 55, 1294 }: Central Line L(55, 1294) { 65, 1363 }: Central Line L(65, 1363) { 133, 1838 }: Central Line L(133, 1838)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.6001, 0.1762) X_122 = -OF-MEDIAL-TRIANGLE (0.5211, -0.0042) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6494, 0.2495) X_107 = Ψ(SYMMEDIAN POINT, ORTHOCENTER) (0.5910, 0.2885) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5940, 0.0549) X_1294 = COLLINGS TRANSFORM OF X(122) (0.4090, -0.8379) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6417, 0.2223) X_1363 = BRISSE TRANSFORM OF X(107) (0.6738, 0.0139) X_133 = INTERSECTION OF LINES X(4)X(74) AND X(5)X(122) (0.6120, 0.5590) X_1838 = ZOSMA TRANSFORM OF X(35) (0.6228, 0.4241) X_3324 = INCIRCLE TRANSFORM T(X(822)) (0.6361, 0.2584)
A
B
C
X12
X122
X56
X107
X55
X1294
X65
X1363
X133
X1838
X3324
Kimberling (6, 9, 13) | AB = 1
X3324 (INCIRCLE TRANSFORM T(X822 ) ) 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
\(f(a,b,c) = a(bw - cv)^{2}/(b + c - a) : b(cu - aw)^{2}/(c + a - b) : c(av - bu)^{2}/(a + b - c)\) , where
\(u : v : w\) =
X822 Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.200392861306\)
▸ Alternate Coordinates1 form
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\) , where \(g(a,b,c) = (b + c)^{2}[a^{6} - a^{4}(2b^{2} - 3bc + 2c^{2}) + a^{2}(b - c)^{2}(b^{2} + c^{2}) - bc(b^{2} - c^{2})^{2}]^{2}/(b + c - a) (E\) . Danneels)
X3324
▸ Incident Central Lines5 lines
▸ Functional Relations2 relations
