Mascheroni construction

Question

There are two points in one line and a point C which doesn't lie on the line AB. I have to construct a point D such that it is intersection of the line AB and a line which is perpendicular to the line AB and points C and D lies on this perpendicular line. I can only use compass and can't link (match) the points. It's on the picture. Thanks for any help.

Answer 1

Following is a construction based on the method described in this answer.
At the end is a picture illustrating the configuration/construction.

• Construct two circles (in red) passing through $C$ centered at $A$ and $B$ respectively.
  These two circles intersect at $C$ and another point $D$.
• Construct a circle (in orange) centered at $C$ passing through $D$.
• Construct a circle (in green) centered at $D$ passing through $C$.
• Start from $D$, following the method of constructing a regular hexagon.
  After two more circles, one find the point $E$ on the orange circle antipodal to $D$.
• Construct a circle (in blue) centered at $E$ passing through $D$.
  This circle intersect the green circle at two points $F$ and $G$.
• Construct two circles (in magenta) through $D$ centered at $F$ and $G$ respectively.
  They intersect at $D$ and another point $H$.

We have construct totally nine circles. The final point $H$ is lying on line $AB$ and line $CH$ is perpendicular to $AB$. i.e. $H$ is the point we seek.