 In any triangle, the radius of the incircle is one-third of the harmonic mean of the altitudes.For any point P on the minor arc BC of the circumcircle of an equilateral triangle ABC, with distances "q" and "t" from B and C respectively, and with the intersection of PA and BC being at a distance "y" from point P, we have that "y" is half the harmonic mean of "q" and "t".In a right triangle with legs "a" and "b" and altitude "h" from the hypotenuse to the right angle, is half the harmonic mean of and .