Given a straight line, a point and a circle (on the same side of the line as the point), construct a circle...

geometry/construction/circle.through.point New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

Given a straight line, a point and a circle (on the same side of the
line as the point), construct a circle that touches the line, the
circle and passes through the point.

You may not take any measurements or perform any calculations.

-- Manish S Prabhu <mprabhu@magnus.acs.ohio-state.edu>

Show solution

1. Draw a line parallel to the given line (call this the "parallel")
2. Drop the perpendicular from the given point to the given line.
3. Draw a radius of the circle and produce outside of the circumference.
4. With centre at the intersection of the circumference and the radius
   and length equal to the perpendicular previously constructed strike
   an arc on the radius produced.
5. With centre at the centre of the given circle and radius equal to the
   distance from the centre to the intersection constructed in (4) draw
   a circle.
6. With centre at the intersection of the circle constructed in (5) and
   the "parallel" and radius equal to the length of the perpendicular,
   draw a circle.  This is the required circle.

-- Brice Wightman <am432@FreeNet.Carleton.CA>

[ Editor: the posting does not say how far from the given line the
"parallel" of step 1 is drawn, and Prabhu's own solution was not
posted. ]