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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.