Geometry Problem 766: Triangle, Altitudes, Exradii, Three Exradius, Equal Harmonic Mean. Level: High School, College.

The figure shows a triangle ABC with the
altitudes h_{a}, h_{b}, h_{c} and the exradii r_{a}, r_{b}, r_{c}. Prove that the
harmonic mean of the altitudes is equal to the harmonic mean of the exradii,
therefore,
.