Area cartograms are transformed maps that display data of regions using map area. Since their construction and usage have some difficulties, their simplified form, circle area cartogram, has been proposed. Circle area cartograms omit to represent the shapes and contiguity of regions, and consequently achieve their simple construction method. The simplicity in their construction makes them popular, as some statistical software has adopted them as one of data visualization options. However, their previous solution sometimes outputs cartograms that are difficult to read, since it does not necessarily retain the geographical distribution of regions. Then we propose a new construction method of circle area cartogram that preserves geographical distributions of regions and creates readable cartograms, and show some examples of applications.