# Another Problem using Heron's

Geometry Level 3

Let $$\triangle ABC$$ have a circle inscribed inside of it such that the circle is tangent at points $$X$$, $$Y$$, and $$Z$$ along sides $$AB$$, $$AC$$, and $$BC$$, respectively. Let $$AX=3$$, $$BZ=4$$, and $$CY=5$$. Find the area of $$\triangle ABC$$.

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

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