Geometric Constructions 12

Given
the midpoint C of a line segment AB, construct a line parallel to AB passing
through a given point D using ruler only.

The
straight lines l and m are parallel, construct the midpoint of A and B
on m using ruler only.

Through
the point A lying outside the given straight line l and m, draw a straight
line parallel to the given ones using ruler only.

Given
A, B on m and l parallel to m, construct C on m with AB = BC using ruler
only.

Given a
circle and its center, construct an inscribed square using ruler only.

Given
two points, construct its midpoint using the compass alone.

Construct
the inversion of a point with respect to a circle using the compass
alone. (You may assume the point lies outside the circle.)

Construct
the inversion of a straight line with respect to a circle using the
compass alone. (You may assume the line lies outside the circle.)

Let
circle A passes through the center of circle B. Construct the inversion
of A with respect to B using the compass alone. (Find two distinct
points of the inversion.)

Suppose
that circle A does not pass through the center of circle B. Construct the
inversion of A with respect to B using the compass alone.

Construct
the circumcircle of a triangle using the compass alone.

Given
a circle but not its center, find its center
using the compass alone.

Divide a circle into four equal parts in five steps using the compass
alone.

Given one side, to construct the other two corners of the square using
the compass alone.

Given a diagonal, to construct the square using the compass alone.

Construct the vertices of a regular pentagon using the compass alone.
Related Sites
http://www.math.niu.edu/~rusin/knownmath/96/mascheroni
http://www.math.niu.edu/~rusin/knownmath/97/mascher
http://forum.swarthmore.edu/dr.math/problems/bau11.15.95_2.html
WHO
WAS GEORG MOHR?
Mascheroni's
construction is taught in C&O 408 "History of Mathematics"
MATH
343 Projective and Inversive Geometries
64513
The Joys of Geometry
Biography
of Lorenzo Mascheroni
Biography
of Georg Mohr