## X(1339) (NAGEL-SCHRÖDER POINT)

 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.

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

 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = (b+c-2a)[4bc(b+c-a) - (a+b+c)(b2 + c2 - a2)]/(b+c-3a)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

Let X'Y'Z' be the extouch triangle of ABC; viz., X' is where the A-excircle meets line BC, and X'Y'Z' is the pedal triangle of X(40). Let I = incenter of ABC. The circles (AIX'), (BIY'), (CIZ') concur in two points: I and X(1339). (Jean-Pierre Ehrmann, Hyacinthos #6545)

X(1339) lies on this line: 1,474

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