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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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