Question

Draw a diagram in which segment AB intersects segment CD equals segment CB

Answer 1

You just have to draw to lines similar in length, and then enlarge one of them to become the AB section, while the other one indicates the starting point for C. You've an example in the attached file :)

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Answer 2

The correct diagram is attached.

Explanation:

Using technology (such as Geogebra), first construct a line segment.  Name the endpoints C and D.

Construct the perpendicular bisector of this segment.  Label the intersection point with CD as B, and create another point A above it.

Measure the distance from C to B and from B to D.  They will be the same.

Measure the distance from A to B.  If it is not the same as that from C to B, slide A along line AB until the distance is the same.

Using a compass and straightedge:

First construct segment CD, being sure to label the endpoints.

Set your compass a little more than halfway from C to D.  With your compass set on C, draw an arc above segment CD.

With your compass set on D (the same distance as before) draw an arc above segment CD to intersect your first arc.  Mark this intersection point as E.

Connect E to CD using a straightedge; mark the intersection point as B.

Set your compass the distance from C to B.  With your compass on B, mark an arc on EB.  Mark this intersection point as A.

AB will be the same distance as CB and BD.