A Sangaku related to Malfatti's Problem

What is the radius of the incircle of the triangle in terms of the radii of the three “kissing circles” of the Malfatti problem (see, e.g. http://ggbtu.be/m593233)? This problem was proposed by the Japanese mathematician TAKATADA Shichi on a sangaku (算額 mathematical tablet hung on a shrine or a temple as a kind of offering) in the Meiseirinji Temple (明星輪寺) in Ogaki City (大垣市).