The solution is indicated by the figure. The triangles AEF and BCD are constructible in this order from the data. First AEF is a right angled triangle with EF = r

But s-c = (a+b+c)/2 - c = (a+b-c)/2 = (a/2) + (b-c)/2. From this we determine the length (b-c) = DC. Knowing also BC = a and the angle at D, we can construct BDC. From this the construction of ABC is obvious.

TriangleBisectorConstruction.html

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