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 3 hours ago by Genady

[Trurl]

3 hours ago, Genady said:

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.

2 arcs of length AJ, if J is the midpoint of AB, equal the length of AB.

You don’t have a straight edge so you have to draw an arc of length AB from point B to determine the line.

Ask @studiot , is this how you would make these geometric constructions?

I thought finding the midpoint of AC was pretty straightforward. But if you are doing this for the first time it is difficult.

You could just mark a line of AB from point B and it would give you the distance. However without a straight edge you need a second arc because you cannot just draw a straight line,

Edited 18 minutes ago by Trurl
Missed letter