# This triangle is arbitrary so how do we determine the circumradius?

Geometry Level 5

In $$\Delta ABC$$, circle $$\Gamma_1$$ passes through $$A$$ and $$B$$, and is tangent to $$BC$$. Circle $$\Gamma_2$$ passes through $$A$$ and $$C$$, and is tangent to $$BC$$. Let the radii of these two circles be 12 and 15 units respectively. If the circumradius of $$\Delta ABC$$ can be represented as $$a \sqrt{b}+c$$, where the surd has been simplified completely and $$a$$, $$b$$ and $$c$$ are integers, find $$a+b+c$$.

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