A tangent to a circle with a straight edge

Question

Given a circle on an Euclidean plane and a point $A$ outside the circle, find a line through $A$, tangent to the circle.
You're allowed to use a straight edge only.

Answer 1

Draw two lines through $A$, crossing the circle. For the next step to be possible, the lines need be in different distances from (unknown...) center of the circle.
Name the intersections of one line and a circle $B$ and $C$, for the other line: $D$ and $E$:

Find a point $F$ at the intersection of lines $BD$ and $CE$, and $G$ at the intersection of $BE$ and $CD$:

Now find $H$ and $J$ as intersections of the line $FG$ with the circle:

Voilà: lines $AH$ and $AJ$ are tangent to the circle.

Answer 2

Generally speaking, Mohr-Mascheroni theorem asserts that whatever constructible by compass and straightedge can also be constructed by straightedge only. Of course, if you want to construct a circle, you surely need to satisfy with constructing 3 distinct points on it.