How to construct the midpoint trajectory between a point on a circle and any point on the geometric sketchpad

Explore the trajectory of the midpoint between a point on the circle and any point. Finding the trajectory of the midpoint between a point on the circle and any point can be applied to various geometric problems and designs. PHP editor Zimo will introduce you to a simple method of constructing this trajectory using the geometric sketchpad. By following the steps below, you can understand the nature of trajectories and explore their potential applications.

Construct a circle O and pick a point A on the circle. Open the geometric sketchpad, select the [Circle Tool] on the left sidebar and draw a circle O in the working area. Use the [Point Tool] to pick any point A on the circle.

Pick any point B and construct line segment AB. Use the [Point Tool] to draw a point B arbitrarily in the blank area, select points A and B in turn, click the [Construct] menu on the upper menu bar, and select the [Line Segment] command from its drop-down option, thus constructing the line segment AB.

Construct the midpoint M of line segment AB. Use the move tool to select line segment AB, click the [Construction] menu on the upper menu bar, and select the [Midpoint] command from its drop-down option, thus obtaining the midpoint M of the line segment.

Construct the trajectory. Use the move tool to select point A and point M in sequence, click the [Construction] menu in the upper menu bar, and select the [Trajectory] command from the drop-down option. This way you will get the motion trajectory of midpoint M,

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