Maybe your question is, why does a force perpendicular to the motion produce a circular orbit? If so, the answer is that an object moving at constant speed in a circle has an acceleration always pointing toward the center of the circle. To see that, analyze the two components of the circular motion (x and y motion) separately, and analyxe the accelerations of the x and y motion separately, and then add the results you got for the acceleration together-- you should see that it always points toward the center.