The figure shows a triangle ABC with the inradius
r and the
altitudes h_{a}, h_{b}, h_{c}. Prove that the inradius is one-third the
harmonic mean of the altitudes, therefore,
\(\dfrac{1}{r}=\dfrac{1}{h_{a}}+\dfrac{1}{h_{b}}+\dfrac{1}{h_{c}}\)
Triangle's inradius
One-third harmonic mean of
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