Here is a shaded crescent formed by two internally tangent circles. Point O is the the center of the larger circle. The width at points B and B' is five units. At point A, the width is 9 units. Find the lengths of the two circle's diameters.
I have included the image that was given. Let $r_1$ and $d_1$ refer to the radius and diameter of the larger circle and let $r_2$ and $d_2$ refer to the radius and diameter of the smaller circle.
mOD= 4.5, because that is where the center of the smaller circle is. Since the two circles are touching and width of the crescent at A is 9. So, the line drawn in from D would be the radius of the smaller circle.
A right triangle is formed, so I could the use Pythagorean Theorem to find $r_2$.
$d_1$= 2 x +10
$d_2$= 2 x +9
The problem is that I don't know where to go from here. Am I even on the right track? Any help on how to finish the problem will be appreciated.