# construction problem with compass

There is given a line (AB) , a point C in the line $C \in (AB)$ and a circle $\Omega$ Construct the circle $\omega$ tangent with $\Omega$ and also tangent in C with (AB) .It should be done with ruler and compass. I can draw (OC) that intercepts $\Omega$ in E. Than I draw a perpendicular line with (OC) in E. I don't know what else to do. • It is not clear what you are trying to do here. Can you clarify your question? – N. Owad Nov 15 '16 at 17:14
• I think it is impossible with a line and a circle put in that positions.. – MattG88 Nov 15 '16 at 17:19
• I am trying to draw a circle $\omega$ tanget with the line (AB) in point C and also tangent with the circle $\Omega$ . Point C, line (AB) and $\Omega$ are alredy given – alana Nov 15 '16 at 17:22
• You want to do that by just "compass and ruler" or by analytic geometry? – G Cab Nov 15 '16 at 17:28
• It's possible to construct with ruler and compass if you're given a unit length. This construction only involves square-roots, addition, and division, all of which can be done via ruler and compass. – Hrhm Nov 15 '16 at 17:29

Imagining the circle we want expanding by the radius of $\Omega$, we see that a circle with the same center goes through the center of $\Omega$ and a $C$ shifted perpendicular to $AB$ by the radius of $\Omega$.
Draw line $CD$ perpendicular to $AB$ through $C$ and then draw the perpendicular bisector of the center of $\Omega$ and the shifted $C$. The circle we want is centered at the intersection of the two lines. 