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Substitute all known relations in result


How do I make mathematica to display results with all known
relations / variables?
E.g. if a result is
and before I'd defined
   r = x^2+y^2
I'd like mathematica to display the result rather as "r".

And: I'd like mathematica to do this for each relation defined before
w/o specifying every possible replacement.

Any help much appreciated.

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