Symmetry and Splitting of a Circle

Draw a circle centered at F with radius 4.5 and mark a point E on it. Also draw a circle centered at A with radius 4 and let its center be C; connect A to C to indicate a reference direction. Construct additional geometry around the circle centered at F and a circle of radius 3 centered at G: draw a line through F determined by points F and G (i), then construct the perpendicular line through F (j). Intersect this radius-3 circle with i and with j to obtain the key intersection points (such as H, I, J and the points on the other intersections like B, D, K, L, M, N). Use rotation about F by 30° to rotate G to G′ and again rotate G′ to G′′, then draw the lines through G′–F and G′′–F. Finally, use these boundary points on the circles to form the sector at F with rays toward Q and the corresponding rotated directions.