X3517

EULER LINE INTERCEPT OF LINE X154X_389

X3517 = homothetic center of tangential triangle and mid-triangle of orthic and circumorthic triangles
< 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) circumcircle: Circumcircle of △ABC { 2, 3 }: Euler Line { 154, 389 }: Central Line L(154, 389) { 231, 1609 }: Central Line L(231, 1609) { 1147, 1351 }: Central Line L(1147, 1351) { 1181, 1495 }: Central Line L(1181, 1495) { 52, 3167 }: Central Line L(52, 3167) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_2 = CENTROID (0.5374, 0.2000) X_4 = ORTHOCENTER (0.6122, 0.3958) X_154 = -CEVA CONJUGATE OF X(6) (0.4807, -0.3954) X_389 = CENTER OF THE TAYLOR CIRCLE (0.6078, 0.2800) X_231 = -CEVA CONJUGATE OF X(128) (1.0375, 0.6458) X_1609 = TCC-PERSPECTOR OF X(19) (0.7601, 0.5316) X_1147 = ISOGONAL CONJUGATE OF X(847) (0.8329, 0.3027) X_1351 = REFLECTION OF X(3) IN X(6) (0.7000, 0.4324) X_1181 = 2nd SARAGOSSA POINT OF X(3) (0.5894, 0.1559) X_1495 = CROSSSUM OF X(2) AND X(30) (0.8194, 1.4855) X_52 = ORTHOCENTER OF ORTHIC TRIANGLE (0.7155, 0.4580) X_3167 = -CEVA CONJUGATE OF X(3) (0.9439, 0.3696) X_3517 = EULER LINE INTERCEPT OF LINE X(154)X(389) (0.6463, 0.4848) A B C X3 X2 X4 X154 X389 X231 X1609 X1147 X1351 X1181 X1495 X52 X3167 X3517 (a, b, c) = (5, 6, 7) | AB = 1

X3517 (EULER LINE INTERCEPT OF LINE X154X_389) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = 3 \cos A - 2 \sec A\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(0.704857473893\)
▸ Incident Central Lines9 lines

{2, 3}, {52, 3167}, {154, 389}, {231, 1609}, {1147, 1351}, {1181, 1495}, {1384, 2207}, {3053, 3199}, {3357, 3426}

▸ Functional Relations2 relations

  • X3517 = circumcircle-inverse of X37942

  • X3517 = homothetic center of tangential triangle and mid-triangle of orthic and circumorthic triangles

Notes

As a point on the Euler line, X3517 has Shinagawa coefficients \((3F, -2E - 3F)\).