Hans Walser, [20170705]

Collinear points

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