1981 IMO Problems/Problem 1
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is a point inside a given triangle . are the feet of the perpendiculars from to the lines , respectively. Find all for which
We note that is twice the triangle's area, i.e., constant. By the Cauchy-Schwarz Inequality,
with equality exactly when , which occurs when is the triangle's incenter, Q.E.D.
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.