STRAIGHT-LINE AND COMPASS CONSTRUCTIONS.

Problem 2

2. Given a straight line and a point on that line, construct a line at right angles to the original line passing through that point.

Solution

1. Let the line be A and the point on A be b.
2. Draw a circle of arbitrary radius centred on b.
3. Let the points of intersection of this circles and A be c and d.
4. Draw two circles, centres c and d, of radius cd.
5. Let the points of intersection of these circles be e and f.
6. The line through e and f intersects A at a right-angle and passes through b, as required.