Awesome geometry -4

Geometry Level 4

In a right angled triangle \(\triangle ABC\) with \(\angle C=90^\circ\) with \(r + r_A + r_B = r_C = 35 \).

Find the perimeter of \(\triangle ABC\).

Details and Assumptions:

  • \(r\) is inradius.

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

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