# We’ve come a long way from where we began

Geometry Level 3

In a triangle $$\triangle ABC$$ with $$r_A = 5 ,r_B = 12, r_C =20$$, let $$\Phi$$ denote its perimeter.

Find the value of $$10 \Phi$$.

Details and Assumption:

• $$r_A , r_B , r_C$$ are radii of excircles opposite to vertices $$A,B,C$$.
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