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Problem 40.
Triangle, Incenter, Excenter. Level: High School, SAT
Prep, College 
In
triangle ABC, the
angles
A and B measure 80 and 40 respectively, I
is the
incenter and E the
excenter. AB and CE meet at D. If BC = a, AC = b and CI = d,
prove
that
.

Try a purely geometric proof.
Trigonometry can come in handy quite often, especially when
dealing with angles.
Hints: See
Problem 40 Geometry Help
Using the deductive method, we start
with a few true statements (the axioms) and use them to prove
dozens, hundreds, or thousands, of other statements (the
theorems). Geometry was organized by the Greek mathematician
Euclid, and his deductive method is still used by mathematicians
today.


