KöMaL 2009 K208

$a$) In the coordinate plane, a circle of radius 5 is drawn about the origin. How many lattice points lie on the circumference of the circle? (A lattice point is a point whose coordinates are both integers.) $b$) Find an integer $r$, such that there are more than 14 lattice points on a circle of radius $r$ centred at the origin. Justify your answer.