newtonian mechanics - Why is the velocity vector perpendicular to the radius vector for projectile motion when the distance from origin is maximal?

After reading this question I have a question of my own:

A solution for the furthest distance from the origin for a projectile motion is to solve $(\frac{y}{x}) \cdot (\frac{dy}{dx})=0 $. Why is it that the velocity vector is perpendicular to the radius for a maximum distance?