# Find the Diameter of a circle from two chords

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.

• The intersection of the perpendicular bisectors of any two chords is the center of the circle. – Andrew Chin Oct 4 at 16:10
• If you're asking how to calculate the length of the diameter from the length of two arbitrary chords, that is impossible. – Matthew Daly Oct 4 at 16:17

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.
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.