Let $O$  be the centre of the circle $x^2+y^2=r^2,$  where $r>\frac{\sqrt{5}}{2}.$  Suppose $PQ$  is a chord of this circle and the equation of the line passing through $P$  and $Q$  is $2x+4y=5.$  If the centre of the circumcircle of the triangle  $OPQ$  lies on the line $x+2y=4,$  then the value of $r$  is ________