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

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, .