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Geometric Problem : Algebraic Proof - Relations Between Distances

Please see the attached file for the actual problem and a graphical illustration.
Let ABC be a right triangle with sides a, b, and hypotenuse c. Let r be the radius of the inscribed circle and ra, rb, and rc be the radii of the escribed circles tangent to sides a, b, and c. What "RELATIONSHIPS" can you discover among the lengths r, ra, rb, rc, a, b, and c. Note that r = (a + b - c)/2


Solution Summary

Relations between geometric distances are found algebraically. The solution is well presented.