Two rights make a...

Geometry Level 4

The legs of two non-degenerate right triangles \(ABC\) and \(DEF\) lie on the boundaries of a quadrant of a set of axes. \(\triangle ABC\) has vertices \(A\left( m,0 \right) \) and \(C\left( 0,n \right) \) and \(\triangle DEF\) has vertices \(D\left( n,0 \right) \) and \(F\left(0,m \right) \).

Let the point where the hypotenuses of \(\triangle ABC\) and \(\triangle DEF\) intersect be \(R\). What is the possible range of values for \(\angle ARF\)?

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