This should be an easy one:

6= R-(sqrt(R^2-50^2)

Solve for R

This is problem for determining an unknown radius from 3 known points where the middle point is 6 units above a line drawn between the outer points that are 50 units apart. Since the word processor here doesn't have algebraic symbols, for clarity, sqrt is square root, and the ^ means squared.
Good luck!!!!
Greg Carter

Firstly, while it's difficult to use math notation here, superscripts and other simple typographic devices are possible -- see the Tips for Posting in this Forum by our moderator, methos.

Your equation can be solved as follows:

Rearrange: sqrt( R² - 50² ) = R - 6
Square both sides: R² - 50² = (R-6)²
Expand: R² - 2500 = R² - 12R + 36
Rearrange: 12R = 2500 + 36 = 2536
Thus R = 2536/12 ≈ 211.333

However, if I understand the problem correctly from your description (sorry I have no way to display a diagram), then the proper equation should be:
sqrt( R² - 25² ) = R-6
In other words, use 25 rather than 50 as one side of a right-triangle construction.

Solving this equation by the same method as above yields:
R = (625+36)/12 = 661/12 ≈ 55.08333

Hope that helps. And welcome to AnswerPool.

Thank you for responding. I should have been able to get this one but my skills have dropped since high school.
Your first answer matched the architects number, but when you presented your second answer, I was confused until I reread my question.
The number 6 units should have been .5 feet and the 50 units should have been 25 feet as you corrected.
Now what do we get?
Thank you again.
Greg Carter

Okay, so now the equation is:
sqrt( R² - 25² ) = R - .5

This yields R = 625.25 exactly.