Do you mean given that c > 1/2 show that r > 1/2?
Rearrange 4c = 1 + 4 r^2 to,
$r = \sqrt{c-0.25}$.
And note that when c=0.5 that r=0.5,
and that $$\sqrt{\cdot}}$$ is an increasing function.
Edit: Re-reading your question I'm not sure I really answered what you asked. Anyway, it's easiest...