Problem

Source: 2010 China South East Mathematical Olympiad

Tags: geometry, geometry unsolved



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 $\frac{FD\times HK}{FH\times DK}=3$


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