Constructing two tangents to the given circle from the point A not on it I'm trying to complete Level 21 from euclid the game: http://euclidthegame.com/Level21/

The goal is to construct two tangents to the given circle from the point A not on it.
So far I've figured that the segments from B to the tangent points must be equal. And of course the triangles AB[tangent point] are right angles.
I'm not seeing how I can find those tangent point, a hint for a good step would be appreciated! I would rather have a hint in the sense of, this is a good step because this and that then just saying what I need to do. I could find those steps without explanation everywhere on the internet if I would like that.

The following solution reflects the figure below. What is slightly interesting about this solution is how it uses only a straightedge.



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*Construct a line $x$ through the given external point $A$ and two different points $X_1$ and $X_2$ on the circle ○$B$. 

*Construct analogous lines $y := \overleftrightarrow{AY_1Y_2}$ and $z := \overleftrightarrow{AZ_1Z_2}$.

*Construct lines $\overleftrightarrow {X_1Y_2}$ and $\overleftrightarrow{X_2Y_1}$. They will intersect at a point $C$.

*Construct lines $\overleftrightarrow {Z_1Y_2}$ and $\overleftrightarrow{Z_2Y_1}$. They will intersect at a point $D$.

*Construct line $\overleftrightarrow{CD}$. They will intersect ○$B$ at two points $E$ and $F$. 

*Construct the desired lines $\overleftrightarrow{EP}$ and $\overleftrightarrow{FP}$ tangent to ○$B$ through $P$. ■
