Please help in assisting me on how to complete this problem. Thanks much!!!
There may be an easier way, but I'd just try to find an equation for the circle, on the cartesian plane.
The green circle I presume has radius 20, so the equation is
$\displaystyle x^2 + y^2 = 20^2 $
The red circle has unknown radius and unknown shift, so the equation is:
$\displaystyle (x - h)^2 + (y - h)^2 = c^2 $
We know 3 points on the red circle, based on your drawing:
$\displaystyle (0,20)$
$\displaystyle (20,0)$
$\displaystyle (-18 \sin \frac{ \pi}{4}, 18 \sin \frac{ \pi}{4})$
Now with this information you can solve for the equation of the red circle and hence the radius.
You could torture yourself working this all out
or you could just use WolframAlpha
circle through (-20, 0), (-9*sqrt (2), 9*sqrt (2)), (0, 20) - Wolfram|Alpha Results