Euclidea 2.7

Euclidea 2.7: Erect a Perpendicular
Given a line $$ \overline{\rm AB} $$ and a point $${\rm C} $$, create a line perpendicular to $$ \overline{\rm AB} $$ that intersects point $${\rm C} $$

Goal: 1L, 3E 

Solution 1L
A very simple solution since there's only one line:


 * 1) Draw the angle bisector of angle $$ \angle{\rm ACB} $$ to finish.

Solution 3E
Create a circle not centered on the line passing through the given point.

Draw a line through the center of the circle and the newly created intersection. (This will show the point on the circle opposite the intersection which is inherently perpendicular to the given line through the given point.)

Draw a line from the given point through the intersection of the new line and circle.