Construct tangent through point on circle in 3 steps

Question

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.

Answer 1

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 !

Answer 2

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