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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