"Problem-Solving and Selected Topics in Euclidean Geometry: in the
Spirit of the Mathematical Olympiads" contains theorems which are
of particular value for the solution of geometrical problems.
Emphasis is given in the discussion of a variety of methods, which
play a significant role for the solution of problems in Euclidean
Geometry. Before the complete solution of every problem, a key idea
is presented so that the reader will be able to provide the
solution. Applications of the basic geometrical methods which
include analysis, synthesis, construction and proof are given.
Selected problems which have been given in mathematical olympiads
or proposed in short lists in IMO's are discussed. In addition, a
number of problems proposed by leading mathematicians in the
subject are included here. The book also contains new problems with
their solutions. The scope of the publication of the present book
is to teach mathematical thinking through Geometry and to provide
inspiration for both students and teachers to formulate "positive"
conjectures and provide solutions.
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