Since we know that all radii in a circle are identical in length, we can equate the measures of the two given radii and solve for x.
We start with the equation:
x + 3 = 3x - 5
To isolate x, we'll simplify the equation:
Subtract x from both sides to get:
3 = 2x - 5
Now add 5 to both sides to further isolate x:
8 = 2x
Finally, divide both sides by 2 to solve for x:
4 = x.
So, x is equal to 4 in our case.
However, we are interested in finding the length of a diameter, not x.
We already know that the radius can either measure x+3 or 3x -5. Substituting x=4 into these expressions, we find that both give us the same result, 7.
This means that the radius of the circle is 7.
Keep in mind the length of a diameter of a circle is twice the length of the radius.
Therefore, if the radius is 7, the diameter would be 2 * 7, or 14.
So, the answer to the problem is:
The length of a diameter of that circle is 14.