TITLE: Radii of inscribed and circumscribed circles in right-angled triangle
QUESTION [5 upvotes]: In a right angled triangle, △ ABC, with sides a and b adjacent to the right angle, the radius of the inscribed circle is equal to r and the radius of the circumscribed circle is equal to R. 
Prove that in △ABC, $a+b=2\cdot \left(r+R\right)$.

REPLY [17 votes]: $$( a - r ) + (b - r ) = 2 R $$