So, I've got a figure, and step one on this is "On the diagonal AC find a point B_1 so that CB_1=AB."
Now, my professor just let people in my class explain that you could do it with a piece of paper or string or ruler etc... but I wondered out loud if it could be done more rigorously, and the TA said she had done it algebraically. This has motivated me to attempt it. Below is figure to use, and what I have done so far. Could someone check my work thus far and let me know if I am on the right track?

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Oh, also. We are given that AP = L, and AB = mL and AC= nL. (L capitalized for readability)

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