## Construct an n-gon (polygon with n sides) for which n given points serve as midpoints of its sides.

Below there is a Java applet that may help you gain insight into the problem. The applet can be in two modes: "Place points" and "Drag mouse", depending on which of the two boxes at the bottom of the applet is checked.

• In the "Place points" mode you should define n points - midpoints of the sides of a polygon. Just click the mouse anywhere inside the applet's rectangle.
• Next you can experiment with the points you thus defined. Change the mode and start dragging the mouse.

If, for whatever reason, you decide to work with a different set of points - press the Reset button and start again.

A word of advice. First of all, start with a simple case. Try just a few points, say, 3, 4, 5. Secondly, attempt to visualize a polygon and then place the points approximately at the middle of its sides. Thirdly, pay attention to the blue circle.

### This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at https://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.

 What if applet does not run?

Explanation

### Various Geometric Constructions

• How to Construct Tangents from a Point to a Circle
• How to Construct a Radical Axis
• Constructions Related To An Inaccessible Point
• Inscribing a regular pentagon in a circle - and proving it
• The Many Ways to Construct a Triangle and additional triangle facts
• Easy Construction of Bicentric Quadrilateral
• Easy Construction of Bicentric Quadrilateral II
• Star Construction of Shapes of Constant Width
• Four Construction Problems
• Geometric Construction with the Compass Alone
• Short Construction of the Geometric Mean
• Construction of a Polygon from Rotations and their Centers
• Squares Inscribed In a Triangle I
• Construction of a Cyclic Quadrilateral
• Circle of Apollonius
• Six Circles with Concurrent Pairwise Radical Axes
• Trisect Segment: 2 Circles, 4 Lines
• Tangent to Circle in Three Steps
• Regular Pentagon Construction by K. Knop