\( \triangle ABC \) has side lengths \( AB=20 \), \( BC=15 \), and \( CA=7 \). Let the altitudes of \( \triangle ABC \) be \( AD \), \( BE \), and \( CF \). What is the distance between the orthocenter (intersection of the altitudes) of \( \triangle ABC \) and the incenter of \( \triangle DEF \)?

Let's think step by step and output the final answer within \boxed{}.
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