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2010 smo (3)

Source: 2010 China South East Mathematical Olympiad

July 18, 2011
geometrygeometry unsolved

Problem Statement

The incircle of triangle ABCABC touches BCBC at DD and ABAB at FF, intersects the line ADAD again at HH and the line CFCF again at KK. Prove that FD×HKFH×DK=3\frac{FD\times HK}{FH\times DK}=3
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