In the figure below, BAC is a right triangle with the incircle and the three excircles. If s is the semiperimeter, points D, E, F, G, H, J, K, L, M, and N are the points of tangency, and r_b  and r_c are de exradii relative to the legs, prove that:
r_b = s - c = AD = AE = BF = BH = CJ = CL, similarly r_c = s - b = AM = AG = CH = CN = BK = BL.
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