Level 16: Given a line, a line segment CD, and a point O. Construct a circle with center O that cuts off a segment congruent to CD on the given line.

Hint: The same old hint – perpendicular bisector of chord pass through center.

Solution: The segment cuts off by the required circle is a chord, and the perpendicular bisector of the chord must pass through center. So let construct the perpendicular bisector by constructing the line pass through O perpendicular to the given segment. That gives us the point J. The point J bisect the chord, and the chord must have length CD, so just find the midpoint of CD (name it E), and then draw a circle with center J with length CE, that gives us the point K, the circle with center O and radius OK give us the solution.