In search of `the Japanese theorem' (Q2482926)

The so-called ``Japanese theorem'', also called ``Chinese theorem'' and ``Maruyama's Theorem'', states that the sum of the radii of the incircles of the triangles issuing from the triangulation of a cyclic polygon made by drawing lines from one of its vertex is independent of the vertex chosen. It is first found in articles published in [Mathesis (3) 5, 268--269 (1905)] and [Arch. Math. Phys. 9, No. 3, 308--310 (1905; JFM 36.0542.02)]. It is attributed (rather fancifully it would seem) to a certain Chinese mathematician which has never been identified precisely.