What is minimum radius of circle given chord length?

Question

What is minimum radius of circle given chord length (Fig.)

I started by setup two line perpendicular to each other.

And find out some area of triangle , then find radius of circle from triangle inscribe in circle formula.

I don't know how this could be correct answer please give any advice for me.

Thank you in advance.

Answer 1

If you don't know anything else about the two line segments $AB$, $AC$, and $CD$ except their lengths, then the minimum radius will be half the length of $AB$ (which at its longest is a diameter of the circle).

So, $(1/2)(2+5) = 7/2.$