Geometry, Theorems and Problems

 Problem 207. Right Triangle, Hypotenuse, Inradius, Exradius relative to the hypotenuse

In the figure below, BAC is a right triangle of hypotenuse BC = a. If r is the inradius, ra is the exradius relative to the hypotenuse, and the points D, E, F, and G are the points of tangency, prove that: a = DG = EF = ra - r.
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Right triangle, hypotenuse
 

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