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.
by
Leonardo Joau