We construct an arbitrary triangle. We give an extra point P and we construct the symmetricals P1,P2, P3 of such point with respect to the three sides of the triangle. Dragging point P we find that some positions yield P1,P2,P3 aligned.

Automatic Solution

Step 1

Now let us consider the triangle of vertices (O,O), (l,O), (a,b) and an arbitrary point (x,y). We consider the symmetrical of such point with respect to the three sides of the triangle, call them, respectively (X,Y),(Z,W), (x,-y).

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