X3742

X3175com[n(INCENTRAL)*n(MEDIAL)]

X3742 = reflection of X3740 in X2
< 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) { 3740, 2 }: Central Line L(3740, 2) { 2, 210 }: Central Line L(2, 210) { 1, 474 }: Central Line L(1, 474) { 37, 982 }: Central Line L(37, 982) { 57, 1001 }: Central Line L(57, 1001) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3740 = com[n(INCENTRAL)*n(MEDIAL)] (0.5150, 0.1733) X_2 = CENTROID (0.5374, 0.2000) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_1 = INCENTER (0.5714, 0.2333) X_474 = EULER LINE INTERCEPT OF LINE X(10)X(56) (0.5441, 0.2176) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_982 = INTERSECTION OF LINES X(1)X(3) AND X(2)X(38) (0.5508, 0.1955) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_1001 = MIDPOINT OF X(1) AND X(9) (0.5412, 0.1974) X_3742 = com[n(INCENTRAL)*n(MEDIAL)] (0.5599, 0.2266) A B C X3740 X2 X210 X1 X474 X37 X982 X57 X1001 X3742 (a, b, c) = (5, 6, 7) | AB = 1

X3742 (X3175com[n(INCENTRAL)*n(MEDIAL)]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(a(b^{2} + c^{2} - ab - ac - 4bc)\)
Search Value (6, 9, 13): \(1.966408284981\)
▸ Incident Central Lines21 lines

{1, 474}, {2, 210}, {31, 3246}, {37, 982}, {55, 3306}, {57, 1001}, {65, 3616}, {72, 3624}, {86, 1431}, {142, 2886}, {171, 1279}, {244, 1962}, {375, 2810}, {405, 3338}, {517, 549}, {614, 940}, {758, 942}, {958, 3333}, {1155, 1621}, {1698, 3555}, {3057, 3622}

▸ Functional Relations3 relations

Notes

Let TaTbTc be the intouch triangle. Let

  • AaAbAc = A-extouch triangle, and define BaBbBc and CaCbCc cyclically

  • Ab' = TbTc∩BbBc, and define Bc' and Ca' cyclically

  • Ac' = TbTc∩CbCc, and define Ba' and Cb' cyclically

Then X3742 = centroid of {Ab',Ac',Bc',Ba',Ca',Cb'}. (Randy Hutson, September 14, 2016)