Hans Walser, 
Idea: Abdilkadir Altintas
Let a be a half circle with base b and l a line orthogonal to b (Fig. 1).
Fig. 1: Half circle and orthogonal line
We draw a circle c of arbitrary radius touching the half circle a and the line l (Fig. 2a).
Fig. 2: A circle and three collinear points
Now the two touching points and one endpoint of the half circle are collinear (Fig. 2b).
The figure 3 gives a proof without words.
Fig. 3: Proof without words