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.
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Solution
![](https://mirangu.com/wp-content/uploads/2023/10/CrazyHatSolution.jpg)
Note that this puzzle can be generalised to any chord and tangent, as was pointed out by Matthew Arcus.
![](https://mirangu.com/wp-content/uploads/2023/10/CrazyHatGeneral.jpg)