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Math Prize 2012 Problem 10

Source:

September 24, 2012

Problem Statement

Let △ABC\triangle ABC be a triangle with a right angle ∠ABC\angle ABC. Let DD be the midpoint of BC‾\overline{BC}, let EE be the midpoint of AC‾\overline{AC}, and let FF be the midpoint of AB‾\overline{AB}. Let GG be the midpoint of EC‾\overline{EC}. One of the angles of △DFG\triangle DFG is a right angle. What is the least possible value of BCAG\frac{BC}{AG}?
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