Philo Line

Eric W. Weisstein
January 11, 2002

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PlaneGeometry/PhiloLine.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/PhiloLine.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Figure

<<PlaneGeometry`

Solve[{r^2 Sin[p]^2+x^2==l^2,
		h^2-l^2==(r Cos[p]+x)^2-(l+dl)^2,
		(2l+dl)^2==h^2 Sin[t]^2+(r Cos[p]+x-h Cos[t])^2,
		(h^2-l^2)+dl^2==r^2},{x,l,dl,h}]

Philo[t_,p_,r_]:=Module[
		{soln,x,l,dl,h,ext=1.1,pt},
		soln=FindRoot[{r^2 Sin[p]^2+x^2==l^2,
		h^2-l^2==(r Cos[p]+x)^2-(l+dl)^2,
		(2l+dl)^2==h^2 Sin[t]^2+(r Cos[p]+x-h Cos[t])^2,
		(h^2-l^2)+dl^2==r^2},{x,1},{l,1},{dl,.5},{h,1}];
		Print[soln];
		pt={r Cos[p]+x-(l+dl)/l x,(l+dl)/l r Sin[p]} /. soln;
		Graphics[{
								{PointSize[.02],Point[r{Cos[p],Sin[p]}],
				Point[pt]},
				{Thickness[.01],Line[{{0,0},ext(x+r Cos[p]){1,0} /. soln}],
				Line[{{0,0},ext h{Cos[t],Sin[t]} /. soln}]},
				Line[{{x+r Cos[p],0},h{Cos[t],Sin[t]}}/.soln],
				{Dashing[{.02,.02}],
				Line[{{0,0},pt}]}
				}]
	]

point[{x_,y_}]:=Circle[{x,y},.015]

Show[
		Philo[40. Degree,12.Degree,1.] /. Point->point,
	AspectRatio->Automatic]