X3328
INCIRCLE TRANSFORM T(X2291 )
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) { 55, 1308 }: Central Line L(55, 1308) { 516, 1317 }: Central Line L(516, 1317) { 517, 1362 }: Central Line L(517, 1362) { 56, 2717 }: Central Line L(56, 2717) { 1, 3322 }: Central Line L(1, 3322)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_7 = GERGONNE POINT (0.5903, 0.2769) X_1638 = TRIPOLAR CENTROID OF X(7) (1.6871, 0.9998) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_1308 = COLLINGS TRANSFORM OF X(661) (1.0102, 0.0916) X_516 = ISOGONAL CONJUGATE OF X(103) (0.7703, 0.7386) X_1317 = REFLECTION OF X(11) IN X(1) (0.4082, 0.3999) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_1362 = BRISSE TRANSFORM OF X(105) (0.4408, 0.4266) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_2717 = SR(X(100), X(103)) (-0.0102, 0.1125) X_1 = INCENTER (0.5714, 0.2333) X_3322 = INCIRCLE TRANSFORM T(X(665)) (0.8047, 0.2285) X_3328 = INCIRCLE TRANSFORM T(X(2291)) (0.3382, 0.2380)
A
B
C
X7
X1638
X55
X1308
X516
X1317
X517
X1362
X56
X2717
X1
X3322
X3328
(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) { 55, 1308 }: Central Line L(55, 1308) { 516, 1317 }: Central Line L(516, 1317) { 517, 1362 }: Central Line L(517, 1362) { 56, 2717 }: Central Line L(56, 2717) { 1, 3322 }: Central Line L(1, 3322)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_7 = GERGONNE POINT (0.6218, 0.2618) X_1638 = TRIPOLAR CENTROID OF X(7) (1.4133, 0.5600) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5714, 0.1429) X_1308 = COLLINGS TRANSFORM OF X(661) (0.9846, 0.1231) X_516 = ISOGONAL CONJUGATE OF X(103) (0.7380, 0.7022) X_1317 = REFLECTION OF X(11) IN X(1) (0.4800, 0.3600) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8038, 0.6743) X_1362 = BRISSE TRANSFORM OF X(105) (0.5231, 0.3846) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6667, 0.3333) X_2717 = SR(X(100), X(103)) (0.0154, -0.1231) X_1 = INCENTER (0.6000, 0.2000) X_3322 = INCIRCLE TRANSFORM T(X(665)) (0.7938, 0.2492) X_3328 = INCIRCLE TRANSFORM T(X(2291)) (0.4062, 0.1508)
A
B
C
X7
X1638
X55
X1308
X516
X1317
X517
X1362
X56
X2717
X1
X3322
X3328
(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) { 55, 1308 }: Central Line L(55, 1308) { 516, 1317 }: Central Line L(516, 1317) { 517, 1362 }: Central Line L(517, 1362) { 56, 2717 }: Central Line L(56, 2717) { 1, 3322 }: Central Line L(1, 3322)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_7 = GERGONNE POINT (0.6026, 0.2652) X_1638 = TRIPOLAR CENTROID OF X(7) (1.5587, 0.5627) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5599, 0.1439) X_1308 = COLLINGS TRANSFORM OF X(661) (0.9504, 0.2172) X_516 = ISOGONAL CONJUGATE OF X(103) (0.7014, 0.7136) X_1317 = REFLECTION OF X(11) IN X(1) (0.4784, 0.3744) X_517 = ISOGONAL CONJUGATE OF X(104) (0.7602, 0.6929) X_1362 = BRISSE TRANSFORM OF X(105) (0.5180, 0.3931) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6411, 0.3392) X_2717 = SR(X(100), X(103)) (0.0496, -0.2172) X_1 = INCENTER (0.5841, 0.2021) X_3322 = INCIRCLE TRANSFORM T(X(665)) (0.7661, 0.2899) X_3328 = INCIRCLE TRANSFORM T(X(2291)) (0.4020, 0.1143)
A
B
C
X7
X1638
X55
X1308
X516
X1317
X517
X1362
X56
X2717
X1
X3322
X3328
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) { 55, 1308 }: Central Line L(55, 1308) { 516, 1317 }: Central Line L(516, 1317) { 517, 1362 }: Central Line L(517, 1362) { 56, 2717 }: Central Line L(56, 2717) { 1, 3322 }: Central Line L(1, 3322)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_7 = GERGONNE POINT (0.6288, 0.2114) X_1638 = TRIPOLAR CENTROID OF X(7) (1.3106, 0.2234) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5940, 0.0549) X_1308 = COLLINGS TRANSFORM OF X(661) (0.8436, 0.1807) X_516 = ISOGONAL CONJUGATE OF X(103) (0.6510, 0.7407) X_1317 = REFLECTION OF X(11) IN X(1) (0.5745, 0.2534) X_517 = ISOGONAL CONJUGATE OF X(104) (0.7243, 0.7243) X_1362 = BRISSE TRANSFORM OF X(105) (0.6036, 0.2595) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6494, 0.2495) X_2717 = SR(X(100), X(103)) (0.1564, -0.7301) X_1 = INCENTER (0.6154, 0.1300) X_3322 = INCIRCLE TRANSFORM T(X(665)) (0.6937, 0.2338) X_3328 = INCIRCLE TRANSFORM T(X(2291)) (0.5371, 0.0262)
A
B
C
X7
X1638
X55
X1308
X516
X1317
X517
X1362
X56
X2717
X1
X3322
X3328
Kimberling (6, 9, 13) | AB = 1
X3328 (INCIRCLE TRANSFORM T(X2291 ) ) 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
\(u : v : w\) =
X2291 Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(3.380590890237\)
X3328
▸ Incident Central Lines5 lines
▸ Functional Relations4 relations
