private Vector3 PlaceOnCircle(Vector3 position) {
    Ray ray = Camera.main.ScreenPointToRay (position);
    Vector3 pos = ray.GetPoint (0f);

    // Making 'pos' local to... ?
    pos = transform.InverseTransformPoint (pos);

    float angle = Mathf.Atan2 (pos.x, pos.z) * Mathf.Rad2Deg;
    pos.x = circle.radius * Mathf.Sin (angle * Mathf.Deg2Rad);
    pos.z = circle.radius * Mathf.Cos (angle * Mathf.Deg2Rad);
    pos.y = 0f;

    return pos;
}