Orthocentre of an acute triangle $ABC$ is at the origin and its circumcenter has the co-ordinates ( $\dfrac{1}{2}, - \dfrac{1}{2}$). If the base $BC$ has the equation $4x - 2y = 5$, then the radius of the circle circumscribing the $\triangle ABC$ is

The distance from the orthocenter (0,0) to the circumcenter (1/2, -1/2) is the Euler line segment. The distance between these points is sqrt((1/2)^2 + (-1/2)^2) = sqrt(1/2). In any triangle, the distance from the circumcenter to a side is R*cos(A). Given the geometry and the line equation, the radius R is calculated as sqrt(5/2).