## Right Triangles in a Square

Draw two lines out from a corner of a square to the opposite sides. Connect the ends of these two lines with a third line, perpendicular to one of the two lines, to form a right triangle. (You may have to adjust the location of the first lines slightly.) Surrounding this central right triangle are three more right triangles.
1. Find such a figure, such that the side lengths of all four triangles are all integers.
2. I expect the previous answer, if it exists, will use some large integers. For a smaller problem, find such a figure, such that just the side lengths of the square and the internal triangle are integers.
3. What is the side length of the smallest square which can contain a 3-4-5 right triangle? A 5-12-13? Is it possible to generalize this?
4. Label the square ABCD, with a side length of s. One acute angle of the central right triangle is at point A. What is the maximum distance the other acute angle can be away from point C?

Source: Original.

Solution
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