The answer is 5√2 in.
Take a look at the attached image. The radius x of the circle is the hypotenuse of the right triangle with sides a and b.
According to the Pythagorean theorem: x² = a² + b²
a is the half of the chord: a = 10/2 = 5 in
b is the distance from the center: b = 5 in
Therefore, the radius x is:
x² = a² + b²
x² = 5² + 5²
x² = 25 + 25
x² = 2·25
x = √(2·25)
x = √2 · √25
x = √2 · 5
x = 5√2 in.
