X3323
INCIRCLE TRANSFORM T(X692 )
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) incircle: Incircle of △ABC { 7, 840 }: Central Line L(7, 840) { 348, 1083 }: Central Line L(348, 1083) { 514, 1358 }: Central Line L(514, 1358) { 518, 1362 }: Central Line L(518, 1362) { 56, 2725 }: Central Line L(56, 2725) { 55, 2736 }: Central Line L(55, 2736)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_7 = GERGONNE POINT (0.5903, 0.2769) X_840 = ISOGONAL CONJUGATE OF X(528) (0.0800, 0.3919) X_348 = ISOTOMIC CONJUGATE OF X(281) (0.4854, 0.1069) X_1083 = MIDPOINT OF X(105) AND X(644) (0.4771, 0.1213) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0761, -0.0329) X_1358 = BRISSE TRANSFORM OF X(101) (0.7869, 0.1440) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_1362 = BRISSE TRANSFORM OF X(105) (0.4408, 0.4266) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_2725 = SR(X(101), X(105)) (0.0347, 0.3116) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_2736 = SR(X(103), X(105)) (0.9653, -0.1075) X_3323 = INCIRCLE TRANSFORM T(X(692)) (0.3587, 0.3291)
A
B
C
X1
X7
X840
X348
X1083
X514
X1358
X518
X1362
X56
X2725
X55
X2736
X3323
(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) incircle: Incircle of △ABC { 7, 840 }: Central Line L(7, 840) { 348, 1083 }: Central Line L(348, 1083) { 514, 1358 }: Central Line L(514, 1358) { 518, 1362 }: Central Line L(518, 1362) { 56, 2725 }: Central Line L(56, 2725) { 55, 2736 }: Central Line L(55, 2736)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_1 = INCENTER (0.6000, 0.2000) X_7 = GERGONNE POINT (0.6218, 0.2618) X_840 = ISOGONAL CONJUGATE OF X(528) (0.1000, 0.3000) X_348 = ISOTOMIC CONJUGATE OF X(281) (0.4576, 0.0000) X_1083 = MIDPOINT OF X(105) AND X(644) (0.4500, 0.0500) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0889, -0.0314) X_1358 = BRISSE TRANSFORM OF X(101) (0.7920, 0.1440) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9533, 0.5666) X_1362 = BRISSE TRANSFORM OF X(105) (0.5231, 0.3846) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6667, 0.3333) X_2725 = SR(X(101), X(105)) (0.0385, 0.1923) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5714, 0.1429) X_2736 = SR(X(103), X(105)) (0.9615, -0.1923) X_3323 = INCIRCLE TRANSFORM T(X(692)) (0.4154, 0.2769)
A
B
C
X1
X7
X840
X348
X1083
X514
X1358
X518
X1362
X56
X2725
X55
X2736
X3323
(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) incircle: Incircle of △ABC { 7, 840 }: Central Line L(7, 840) { 348, 1083 }: Central Line L(348, 1083) { 514, 1358 }: Central Line L(514, 1358) { 518, 1362 }: Central Line L(518, 1362) { 56, 2725 }: Central Line L(56, 2725) { 55, 2736 }: Central Line L(55, 2736)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_1 = INCENTER (0.5841, 0.2021) X_7 = GERGONNE POINT (0.6026, 0.2652) X_840 = ISOGONAL CONJUGATE OF X(528) (0.0333, 0.1794) X_348 = ISOTOMIC CONJUGATE OF X(281) (0.4646, 0.0000) X_1083 = MIDPOINT OF X(105) AND X(644) (0.4503, 0.0413) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0910, -0.0001) X_1358 = BRISSE TRANSFORM OF X(101) (0.7685, 0.1194) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9071, 0.6040) X_1362 = BRISSE TRANSFORM OF X(105) (0.5180, 0.3931) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6411, 0.3392) X_2725 = SR(X(101), X(105)) (0.0056, 0.0748) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5599, 0.1439) X_2736 = SR(X(103), X(105)) (0.9944, -0.0748) X_3323 = INCIRCLE TRANSFORM T(X(692)) (0.3842, 0.2323)
A
B
C
X1
X7
X840
X348
X1083
X514
X1358
X518
X1362
X56
X2725
X55
X2736
X3323
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) incircle: Incircle of △ABC { 7, 840 }: Central Line L(7, 840) { 348, 1083 }: Central Line L(348, 1083) { 514, 1358 }: Central Line L(514, 1358) { 518, 1362 }: Central Line L(518, 1362) { 56, 2725 }: Central Line L(56, 2725) { 55, 2736 }: Central Line L(55, 2736)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_1 = INCENTER (0.6154, 0.1300) X_7 = GERGONNE POINT (0.6288, 0.2114) X_840 = ISOGONAL CONJUGATE OF X(528) (-0.0041, -0.0075) X_348 = ISOTOMIC CONJUGATE OF X(281) (18.0513, 32.3615) X_1083 = MIDPOINT OF X(105) AND X(644) (0.3486, -0.0955) X_514 = ISOGONAL CONJUGATE OF X(101) (1.1917, -0.0133) X_1358 = BRISSE TRANSFORM OF X(101) (0.7451, 0.1212) X_518 = ISOGONAL CONJUGATE OF X(105) (1.0454, 0.5168) X_1362 = BRISSE TRANSFORM OF X(105) (0.6036, 0.2595) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6494, 0.2495) X_2725 = SR(X(101), X(105)) (-0.0515, -0.1289) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5940, 0.0549) X_2736 = SR(X(103), X(105)) (1.0515, -0.4205) X_3323 = INCIRCLE TRANSFORM T(X(692)) (0.4897, 0.1632)
A
B
C
X1
X7
X840
X348
X1083
X514
X1358
X518
X1362
X56
X2725
X55
X2736
X3323
Kimberling (6, 9, 13) | AB = 1
X3323 (INCIRCLE TRANSFORM T(X692 ) ) 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
\(u : v : w\) =
X692 Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.338565297741\)
▸ Alternate Coordinates1 form
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\) , where \(g(a,b,c) = (b - c)^{2}(b^{2} + c^{2} - ab - ac)^{2}/(b + c - a) (E\) . Danneels)
X3323
▸ Incident Central Lines6 lines
{7 840 55 2736 56 2725 348 1083 514 1358 518 1362
▸ Functional Relations1 relation
