The equation of the circle with radius 'r' and center at Origin (0, 0) is expressed as x²+y²=r² … Eq.1.
When the center (0, 0) is moved to the point (3, 2), the equation of the new circle can be expressed as (x-3)²+(y-2)²=r² … Eq.2
The point (5, 4) rests on the circumference of Eq.2, so Eq.2 can be rewritten plugging x=5 and y=4 into the equation. (5-3)²+(4-2)²=r²
That is r²=2²+2²=8. Here, we have the solution: r=8^½ =(4*2)^½=(4^½)*(2^½)=2*(2^½). We omitted (-)2*(2^½) because r>0.
The answer: The length of the radius is 2*(2^½).