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A friend gave me this problem but I have no idea how to approach it.

Suppose you are given a triangle $ABC$. Pick points $P$ inside or on perimeter, such that the perimeter of the triangle $(PA+PB+PC)$ is maximized.

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Hi there, what you're looking for is the Toricelli point. There's a nice method from physics that allows you to understand why the angle subtended by any side of the triangle at P is $120°$ which I wrote up in the second part of my question here: math.stackexchange.com/questions/255464/… – Vincent Tjeng Feb 27 at 9:32
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"The perimeter of the triangle $(PA+PB+PC)$"? $PA$, $PB$, and $PC$ do not form a triangle. – Rahul Narain Feb 27 at 9:51
@VincentTjeng: What you're talking about gives the minimum possible sum. Torricelli point is where the sum of distance from vertices to that point is minimum.! – Inceptio Feb 27 at 12:39
@Inceptio you're right. in that case then P will have to be on one of the vertices, right? – Vincent Tjeng Feb 27 at 14:02
Yeah! That point is where two larger sides converge. – Inceptio Feb 27 at 14:06

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