Question

How many arcs do we need to construct a ${90}^{\circ }$ through a point outside the line?

Answer 1

The steps to construct a ${90}^{\circ }$ through a point outside the line are given below.

Step 1: Take the width of compass greater distance between point P and line AB.

Step 2: With the same length, draw two arcs on the line AB using P as the center.

Step 3: With the same length, draw two arcs above and below the line centered at the point of intersection of one of the earlier arc with the line.

Step 4: With the same length, draw two arcs above and below the line centered at the point of intersection of the other arc with the line.

Step 5: Draw the line through the point of intersection of the two arcs above and the two arcs below.


Therefore, we need 6 arcs to construct a perpendicular line from a point above the line.