How do I find the diameter of this circle?
Since the longest chord has five the diameter has to be bigger than five. I tried adding perpendicular bisectors but was unable to find a triangle to solve in any way to find a radius. I was kind of hoping that I just wasn't looking at it properly and drawing the right lines and perpendicular bisectors would make a nice triangle. But no luck so far. Thank you.
With the information given, there's no way to solve this, because for any circle whose diameter is larger than $5$, there's a way to draw two intersecting chords of lengths $4$ and $5$. If you're really supposed to determine the diameter of THIS particular circle on this piece of paper, you could, I suppose, measure it with a pair of calipers, and then compare to the measured length of DC, etc. But a quick measurement of the lengths in this diagram suggests to me that they are not in the ratio of 4 to 5, so this latter approach can't possibly be what's wanted --- the diagram is evidently meant to show an abstraction of the actual conditions.
One possibility, suggested by the diagram, is that the intersection of the two chords bisects the shorter one. If THAT is given, then you can possibly get somewhere... nope...after a little reflection, I can see that even that doesn't give enough information to get you anywhere.
Any circle with diameter greater or equal $5$ will do. You can simply draw cords of length $4$ and $5$ in any circle which is large enough to allow such cords.
