FontenéFirstTheorem::usage="There is a base triangle and an inner point v. If in the pedal triangle with respect to v and in the medial triangle, their sides are extended, they intersect at three different points. The lines that connect the vertices of the pedal triangle with these points are concurrent at a point where the 9-point circumference and the pedal circumference have one point in common, the point F. References: Wolfram MathWorld: Fontené theorems, Pedal triangle, Pedal circle, Medial triangle, Triangle interior; Personal. ";
In[]:=
Example 1:
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FontenéFirstTheorem[tri={{-2,5},{7,12},{9,-4}},v={5,3}]
PointF

14665
2474
,
2485
2474

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Example 2:
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FontenéFirstTheorem[tri={{0,0},{1,0},{0.3,0.7}},v={0.53,0.3}]
PointF
{0.621101,0.0963303}
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Example 3:
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FontenéFirstTheorem[tri={{-4,-3},{3,-1},{-3,1}},v={-1,-1}]
PointF
-
311
241
,-
581
241

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