1. ## 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.

2. It's the midpoint of BC.

3. Originally Posted by Jeqle
It's the midpoint of BC.
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

4. 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