# 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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