X3676

X650com(INTOUCH TRIANGLE)

X3676 = X647-of-intouch-triangle
< 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 { 57, 649 }: Central Line L(57, 649) { 241, 514 }: Central Line L(241, 514) { 109, 658 }: Central Line L(109, 658) { 513, 676 }: Central Line L(513, 676) { 522, 693 }: Central Line L(522, 693) { 1443, 1447 }: Central Line L(1443, 1447) 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_3939 = com[INVERSE(n(INTOUCH TRIANGLE))] (0.0417, 0.4082) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_649 = CROSSDIFFERENCE OF X(1) and X(2) (-21.0000, 14.6969) X_241 = -LINE CONJUGATE OF X(55) (1.1217, 1.2442) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0761, -0.0329) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_658 = TRILINEAR POLE OF LINE X(1)X(7) (0.3795, 0.5837) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_676 = CROSSDIFFERENCE OF X(3) AND X(101) (1.2449, 0.5665) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_693 = ISOTOMIC CONJUGATE OF X(100) (-25.8163, 8.9981) X_1443 = -BETH CONJUGATE OF X(320) (0.9441, 1.0954) X_1447 = -BETH CONJUGATE OF X(350) (1.1014, 1.0207) X_3676 = com(INTOUCH TRIANGLE) (-4.3265, 3.5993) A B C X1 X3939 X57 X649 X241 X514 X109 X658 X513 X676 X522 X693 X1443 X1447 X3676 (a, b, c) = (5, 6, 7) | AB = 1

X3676 (X650com(INTOUCH TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \((b - c)/(b + c - a) : :\)
Search Value (6, 9, 13): \(1.878120566063\)
▸ Incident Central Lines13 lines

{2, 4468}, {7, 6006}, {11, 3323}, {57, 649}, {109, 658}, {241, 514}, {278, 3064}, {513, 676}, {522, 693}, {918, 3239}, {934, 2222}, {1443, 1447}, {3321, 3322}

▸ Functional Relations7 relations

Notes

Let P1 and P2 be the two points on the Gergonne line whose trilinear polars are parallel to the Gergonne line. P1 and P2 lie on the circumconic centered at X1086 (hyperbola {{A, B, C, X2, X7}}), and circle {{X2, X109, X675}}. The midpoint of P1 and P2 is X1638. X3676 is the barycentric product P1*P2. (Randy Hutson, January 15, 2019)