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I'm stuck in the Euclidea app in level 2.8, which asks:

Given a circle and a point on that circle, construct the tangent through that point using only 3 elemental steps.

Their FAQ already mentions that the steps are circle, circle, line (and these are the only allowed construction steps). The strange thing is that neither the German nor the English Wikipedia describe how to do this construction in only 3 steps, although I think the shortest way should be documented there.

Roland Illig
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  • Is it possible that the exercise begins with a line or ray already drawn from the center of the circle through the point "on the circle"? If so, I can see how circle, circle, line would complete the exercise (the line being the tangent). Not being able to see what is given in this exercise handicaps your Readers. – hardmath Aug 20 '17 at 13:37
  • No, only the circle and the point are given. – Roland Illig Aug 20 '17 at 13:51

2 Answers2

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Mathematics StackExchange has already answered this question, even including a proof based on the inscribed angle theorem, among a few theorems.

PDE
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I would say :

1) Draw a ligne that pass through $P$ and the center of the circle $O$

2) With a compass draw a point that $Q$ s.t. $P$ is the middle of $OQ$.

3) Draw the bisection of $[P,Q]$, and you have it !

Surb
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  • This is the construction already given in Wikipedia. But the Euclidian app claims there is a shorter way, which involves only circles and lines, but not composite steps like bisections. – Roland Illig Aug 20 '17 at 13:50