Two Squares

Pick a point P on the line segment AB and make squares: A side of one square is AP and a side of the other square is PB. Where should the point P be located to satisfy the condition that the sum of the areas of the two squares is a minimum?

The pictures, either configuration:

Discuss and demonstrate alternative solutions or analyses of the problem.

Seven ways to Solvc this. Produce some solutions of your own before looking at this.

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