For an equilateral triangle ABC of side $a$ vertex A is always moving in the direction of vertex B, which is always moving the direction of vertex C, which is always moving in the direction of vertex A. The modulus of their "velocity" is a constant. When and where do they converge.
Attempt. Found the "when" using a physics style approach by "fixing the frame" on one of the vertices. (From this frame, other two vertex are moving towards origin in a straight line and components of their speed along this line can be used to find when the three meet at origin) For the "where" it is difficult using above approach as this is some kind of rotating and shrinking triangle which is difficult to translate.
@all Apologies for bumping this question. I wished to give an answer the bounty but it wont let me until the next 23 hours. For the record: I am not seeking new answers.
Update: A cool example of PSTricks package of $\LaTeX$, for anyone who finds this question later.
Link to code (a .tex file)
And using Pgf/TikZ