CN-SMO 2010 Problem 3

The incircle of triangle $ABC$ touches $BC$ at $D$ and $AB$ at $F$ , intersects the line $AD$ again at $H$ and the line $CF$ again at $K$ . Prove that $\frac{FD\times HK}{FH\times DK}=3$ Attachments:

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Dataset text AI-MO AoPS. Quoted with source.

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