STRAIGHT-LINE AND COMPASS CONSTRUCTIONS.

Problem 7

7. Given a line, and a point not on that line, construct a circle whose centre is that point and which touches (tangentially) the line.

Solution

1. Let the line be A and the point not on A be b.
2. Draw a circle centred on b of sufficient radius to intersect A in two places, c and d.
3. Find the midpoint of c and d according to solution 1.
4. Call this midpoint e; the circle centred on b of radius be is the desired circle.