I'm trying to solve a geometry problem using cevians.
The image shows what the triangle would look like. (Don't follow the scale. On GeoGebra I just drew a random triangle.) The given side lengths should be: $AX=2$, $XP=1$, $YP=3$, $ZP=5$, and $YC=10$.
I want to find the length of $XB$, $BY$, $CZ$, and $ZA$, if possible.
If you can show me how to find one side length, that would be enough.
Ceva's theorem is definitely not enough, and I've tried using the Law of Sines but it gets pretty messy. I think that method should work if I can use the sine addition formula to somehow cancel out the angles, but there are so many triangles that I can't figure out which to focus on.
I don't really know if the problem solvable (I think it is, but I designed this specific problem, so who knows?), and I don't know if there is too much given information where it contradicts other given information.
Thank you