Crazy hat

The diameter of the semicircle is a side of a rectangle. Show that for any such rectangle, and any point along its top edge, the configuration produces three collinear red dots.

Scroll down for a solution to this problem.


Solution by Bob Ruyle.

Note that this puzzle can be generalised to any chord and tangent, as was pointed out by Matthew Arcus.

Generalisation of Crazy Hat.

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