Are tangent points allowed in ruler and compass constructions?

[Trurl]

You could find the midpoint of A and B by adjusting your compass to any distance slightly lager than half AB. With this distance make an arc from A than B. The intersection of the two arcs is the midpoint. Call this midpoint point J.

With the AJ length of the compass from B draw an arc. From any point on this arc draw another arc with length AJ.

With compass size AB draw and arc that intersects the last arc you made. This is BC.

[Genady]

6 hours ago, Trurl said:

You could find the midpoint of A and B by adjusting your compass to any distance slightly lager than half AB. With this distance make an arc from A than B. The intersection of the two arcs is the midpoint. Call this midpoint point J.

With the AJ length of the compass from B draw an arc. From any point on this arc draw another arc with length AJ.

With compass size AB draw and arc that intersects the last arc you made. This is BC.

No, it is not.

[Genady]

12 hours ago, Trurl said:

You could find the midpoint of A and B by adjusting your compass to any distance slightly lager than half AB. With this distance make an arc from A than B. The intersection of the two arcs is the midpoint. Call this midpoint point J.

With the AJ length of the compass from B draw an arc. From any point on this arc draw another arc with length AJ.

With compass size AB draw and arc that intersects the last arc you made. This is BC.

This problem is not asking to find a midpoint of A and B. It asks to find a point C such that B is the midpoint of A and C.

Anyway, here is a drawing according to your steps. It does not seem to work.

 

Edited 1 hour ago by Genady