Minimization

ABC has a right angle at A. Among all points P on the perimeter of the triangle, find the position of P such that
AP+BP+CP
is minimized.

It's the midpoint of BC.

Quote:

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Originally Posted by Jeqle

It's the midpoint of BC.

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Not true, it clearly lies in one of two places, the foot of the altitude from A or at A. The final argument is more subtle

Quote:

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Originally Posted by SimonM

Not true, it clearly lies in one of two places, the foot of the altitude from A or at A. The final argument is more subtle

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Tha answer is P=A. Check the MathLinks solution.