Image:Cevastheorem.jpg

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Picture for Ceva's_Theorem.

The Mathematica code which produced this diagram:

a = {0, 0};
b = {3, 2};
c = {5, 0};
\[Lambda] = 2;
\[Mu] = .5;
p = (b + \[Lambda] c)/(1 + \[Lambda]);
q = (c + \[Mu] a)/(1 + \[Mu]);
r = (\[Lambda] \[Mu] a + b)/(1 + \[Lambda] \[Mu]);
\[Lambda] = \[Mu] + 1/\[Lambda];
x = (c + \[Lambda] r)/(1 + \[Lambda]);
\[Lambda] = 20;
Show[Graphics[{
      Line[{a, b, c, a}],
      Text["A", (\[Lambda] a - p)/(\[Lambda] - 1)],
      Text["B", (\[Lambda] b - q)/(\[Lambda] - 1)],
      Text["C", (\[Lambda] c - r)/(\[Lambda] - 1)],
      Line[{a, p}],
      Line[{b, q}],
      Line[{c, r}],
      Text["D", (\[Lambda] p - a)/(\[Lambda] - 1)],
      Text["E", (\[Lambda] q - b)/(\[Lambda] - 1)],
      Text["F", (\[Lambda] r - c)/(\[Lambda] - 1)],
      PointSize[.008],
      Point[x],
      Text["X", x + {.1, .1}]
      }], TextStyle -> {FontSize -> 30, FontFamily -> Times},
  AspectRatio -> Automatic, PlotRange -> All]

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