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How do Spanish IMO Shortlist Geometry Problems look like?

Source: IMO Shortlist 1993, Spain 2; India TST 1994

March 15, 2006
geometryinradiusincentertrigonometryLaw of SinesIMO Shortlist

Problem Statement

Given a triangle ABCABC, let DD and EE be points on the side BCBC such that ∠BAD=∠CAE\angle BAD = \angle CAE. If MM and NN are, respectively, the points of tangency of the incircles of the triangles ABDABD and ACEACE with the line BCBC, then show that 1MB+1MD=1NC+1NE.\frac{1}{MB}+\frac{1}{MD}= \frac{1}{NC}+\frac{1}{NE}.
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