X(1316) (5th MOSES INTERSECTION)

 Interactive Applet

You can move the points A, B and C (click on the point and drag it).
Press the keys “+” and “−” to zoom in or zoom out the visualization window and use the arrow keys to translate it.

You can also construct all centers related with this one (as described in ETC) using the “Run Macro Tool”. To do this, click on the icon , select the center name from the list and, then, click on the vertices A, B and C successively.

 The JRE (Java Runtime Environment) is not enabled in your browser!

This applet was built with the free and multiplatform dynamic geometry software C.a.R..

 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears            bcf(a,b,c) : caf(b,c,a): abf(c,a,b), where f(a,b,c) is the 1st barycentric given below

Barycentrics    f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a8 + a4b2c2 - a6(b2 + c2) + b2c2(b2 - c2)2

Barycentrics    f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = b2c2(b2 - c2)2 + a4(a2 - b2)(a2 - c2)

X(1316) is the point of intersection, other than X(3), of the Euler line and Brocard circle.
X(1316) is the point of intersection of the Euler line and the trilinear pole of X(98). [P.J.C. Moses, 6/22/04]
X(1316) is the orthogonal projection of X(6) on theEuler line.

X(1316) lies on these lines:
2,3    6,523    250,264    262,842    338,1576

X(1316) = {X(1113),X(1114)}-harmonic conjugate of X(237)
X(1316) = {X(2),X(4)}-harmonic conjugate of X(868).

For a longer list of harmonic conjugates of X(1316), click More at the top of this page.

X(1316) = inverse-in-circumcircle of X(237)
X(1316) = inverse-in-orthocentroidal-circle of X(868)
X(1316) = inverse-in-2nd-Lemoine-circle of X(2451)
X(1316) = crossdifference of any two points on line X(511)X(647)
X(1316) = X(6)-Hirst inverse of X(523)

This is a joint work of
Humberto José Bortolossi, Lis Ingrid Roque Lopes Custódio and Suely Machado Meireles Dias.