I always loved construction problems. I will write a lot about them. Today I talked to my high school math teacher and among other things I mentioned constructions with a compass only. He replied that constructions with a straight edge only are the interesting kind as well. I have never seen one before, so he immediately gave me one to solve. It is relatively simple, but I like it.
You are given an arbitrary circle. A diameter is drawn in this circle. You are also given a point outside the circle. Using straight edge only, construct a perpendicular line from a given point to a given diameter.
When solving, do not forget that a perpendicular line can intercept a diameter itself or its continuation.
I will post a solution in the next post in order not to spoil someone a pleasure to find a solution by oneself.
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