Another Problem using Heron's

Geometry Level 3

Let ABC\triangle ABC have a circle inscribed inside of it such that the circle is tangent at points XX, YY, and ZZ along sides ABAB, ACAC, and BCBC, respectively. Let AX=3AX=3, BZ=4BZ=4, and CY=5CY=5. Find the area of ABC\triangle ABC.

If your answer can be expressed as aba\sqrt{b} where aa and bb are positive integers with bb squarefree, find a+ba+b.

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