1. Derive a formula for, given as input the coordinates for a
line L, finding the point on L closest to the origin. You may use either
Cartesian or Projective coordinates.

2. Let b and c be points in the plane, with origin 0, such that 0bc is a
right angle, and suppose that b' and c' are the images of b and c after
inverting these points through a circle centered at 0. What can you say
about the angles in triangle 0b'c'?

3. If abcd is a convex quadrilateral, specified using n-bit integers for
each Cartesian coordinate of each point, then how many bits of precision
would be needed to accurately specify the point where the two diagonals of the
quadrilateral cross? Could this point be represented precisely using
Cartesian coordinates? With projective coordinates?