Brandon uses the steps below to construct a perpendicular line through a point C on a line segment. He first draws two arcs from point C intersecting the line segment in points A and B.
Step 1: Using the same compass width draw two more arcs from point C, one above and the other below the line.
Step 2: Without changing the compass width, draw two arcs from point B above and below the line segment.
Step 3: Label the point of intersection of the arcs above the line segment as M and below the line as N.
Step 4: Using a straightedge, join point M and point M and point N.

Question

Brandon uses the steps below to construct a perpendicular line through a point C on a line segment. He first draws two arcs from point C intersecting the line segment in points A and B. 
Step 1: Using the same compass width draw two more arcs from point C, one above and the other below the line.
Step 2: Without changing the compass width, draw two arcs from point B above and below the line segment.
Step 3: Label the point of intersection of the arcs above the line segment as M and below the line as N.
Step 4: Using a straightedge, join point M and point M and point N.

ikram002p · Answer

http://www.mathopenref.com/constperpextpoint.html