A geometry problem by Leonardo Joau

Geometry Level 4

\(ABC\) is an isosceles triangle with \(\overline{AB}=\overline{AC}\).

\(\alpha\) and \(\beta\) are two circumferences that have centres in \(\overline{BC}\) and intersects this straight line in points \(B\),\(S\) and \(C\).

The diameters of \(\alpha\) and \(\beta\) are \(\sqrt{2}+1\) and \(1\), respectively.

If \(\measuredangle{BAS}=30^\circ\) find \(\angle{ABP}\).

Enter your answer in degrees.

Note: Image drawn not up to scale.


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