A geometry problem by Leonardo Joau

Geometry Level 5

$ABC$ 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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