Denoting the altitudes of any triangle from sides a, b, and c respectively as h a {\displaystyle h_{a}} , h b {\displaystyle h_{b}} , and h c {\displaystyle h_{c}} , and denoting the semi-sum of the reciprocals of the altitudes as H = ( h a − 1 + h b − 1 + h c − 1 ) / 2 {\displaystyle H=(h_{a}^{-1}+h_{b}^{-1}+h_{c}^{-1})/2} we have[32]