On the circle there are given three distinct points . Construct (using only a straightedge and a compass) a fourth point on such that a circle can be inscribed in the quadrilateral thus obtained.
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On the circle $K$ there are given three distinct points $A,B,C$. Construct (using only a straightedge and a compass) a fourth point $D$ on $K$ such that a circle can be inscribed in the quadrilateral thus obtained.
Source: Međunarodna matematička olimpijada, shortlist 1962
Školjka 
there are given three distinct points 
. Construct (using only a straightedge and a compass) a fourth point 
on