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BMT 2015 Spring - Geometry 9

Source:

December 30, 2021
geometry

Problem Statement

Let ABCABC be a triangle. Suppose that a circle with diameter BCBC intersects segments CACA, ABAB at E,FE, F, respectively. Let DD be the midpoint of BCBC. Suppose that ADAD intersects EFEF at XX. If AB=9AB =\sqrt9, AC=10AC =\sqrt{10}, and BC=11BC =\sqrt{11}, what is EXXF\frac{EX}{XF}?
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