INRADII PROBLEM

Let ABC be a triangle, D a point on BC and r, r_b, r_c the inradii of ABC, ABD, ACD, resp. 1. AB _|_ BC ( ie A = 90 d.), AD _|_ BC (ie AD is the a-altitude) ==> r^2 = r_b^2 + r_c^2
(Old theorem)
2. ΨΗΦ. Πρόβλημα 19