Awesome geometry -4

Geometry Level 4

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

Find the perimeter of ABC\triangle ABC.

Details and Assumptions:

  • rr is inradius.

  • rA,rB,rCr_A , r_B , r_C are radii of excircles opposite to vertices A,B,CA,B,C.

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