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 NagelPoint
 find the Nagel point of a given triangle

 Calling Sequence NagelPoint(N, ABC)

Parameters

 ABC - triangle N - the name of the Nagel point

Description

 • Let H, E, F be the points on the sides BC, CA, AB of triangle ABC such that H is half way around the perimeter from A, E half way around from B, and F half way around from C. AH, BE, CF are concurrent. This point of concurrence is called the Nagel point of the triangle, after C. H. Nagel (1803-1882).
 • For a detailed description of the Nagel point N, use the routine detail (i.e., detail(N)).
 • Note that the routine only works if the vertices of the triangle are known.
 • The command with(geometry,NagelPoint) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geometry}\right):$
 > $\mathrm{triangle}\left(T,\left[\mathrm{point}\left(A,0,0\right),\mathrm{point}\left(B,2,0\right),\mathrm{point}\left(C,1,3\right)\right]\right):$
 > $\mathrm{NagelPoint}\left(N,T\right)$
 ${N}$ (1)
 > $\mathrm{coordinates}\left(N\right)$
 $\left[{1}{,}\frac{{6}{}\sqrt{{10}}{-}{3}{}\sqrt{{4}}}{{2}{}\sqrt{{10}}{+}\sqrt{{4}}}\right]$ (2)