The method of constructing the midpoint trajectory of a point on a circle and any point on the geometric sketchpad

The method of constructing the midpoint trajectory of a point on a circle and any point on the geometric sketchpad

Construct a circle O and take a point A on the circle. Open the geometry artboard, select the left sidebar [Circle Tool] to draw a circle O in the work area, and use the [Point Tool] to take any point A on the circle.

The method of constructing the midpoint trajectory of a point on a circle and any point on the geometric sketchpad

Take any point B and construct the line segment AB. Use the [Point Tool] to draw a point B in the blank space, select points A and B in turn, click the [Construct] menu in the upper menu bar, and select the [Line Segment] command in its drop-down option, so that the line segment AB is constructed.

The method of constructing the midpoint trajectory of a point on a circle and any point on the geometric sketchpad

The midpoint M of the constructed line segment AB. Select the line segment AB with the mobile tool, click the [Structure] menu in the upper menu bar, and select the [Midpoint] command in its drop-down option, so that you get the midpoint M of the line segment.

The method of constructing the midpoint trajectory of a point on a circle and any point on the geometric sketchpad

Tectonic trajectory. Use the movement tool to select point A and point M in turn, click the [Construct] menu in the upper menu bar, and select the [Trajectory] command in its drop-down option, so that you can get the movement trajectory of the midpoint M.

The method of constructing the midpoint trajectory of a point on a circle and any point on the geometric sketchpad

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