  This is the first part of a series of papers aiming to show how trigonometry
and analytic tools can help into tackling demanding Olympiad geometry problems.
We present several novel techniques for tackling hard problems from various
international and national mathematical competitions, and develop the
appropriate theoretical background.
  Several insightful examples and practice problems are included for the reader
to sharpen their problem solving skills. The number of asterisks next to each
problem indicate its (subjective) difficulty level, ranging from (*) (early IMO
problem) to (***) (hard IMO problem), or ocassionaly (****) (too hard for an
IMO problem). Lastly, at the end of the paper we devote a section on providing
some historical information on mathematicians whose names appeared in the
paper.
