Too many tangents!

Geometry Level 4

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 $${ w }_{ 2 }$$.

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