Too many tangents!

Semicircle $AB$ has diameter $d$ , and semicircles $AC$ and $CB$ have diameters $10$ and $d-10$ (so $10<d$ ), respectively. Line $CD$ is perpendicular to line $AB$ .

In the diagram above, inscribe two circles such that one is tangent to semicircles $CB$ and $AB$ and tangent to line $CD$ , and another that is tangent to semicircles $AC$ and $AB$ and tangent to line $CD$ . Call these ${ w }_{ 1 }$ and ${ w }_{ 2 }$ , respectively.

The area of ${ w }_{ 1 }$ is 10 units. Determine the area of ${ w }_{ 2 }$ .