How to draw a nine-point circle using geometric sketchpad

Open the geometric sketchpad and create a new blank sketchpad. In the left toolbar, select the polygon tool to draw △ABC, select the three sides AB, BC, and AC, and select the [Midpoint] command in the [Construction] menu to make three Side midpoints D, E, F.

Select point A and side BC, select [Perpendicular Line] in the [Construction] menu, make a perpendicular line, select side BC and the perpendicular line, select [Perpendicular Line] in the [Construction] menu Intersection point], find the intersection point G which is the vertical foot on side BC; use the same method to find the vertical feet H and I on sides AC and AB.

Select points A and G, select [Straight Line] in the [Construction] menu, and make a straight line AG. Select points B and H, select [Straight Line] in the [Construction] menu, and draw a straight line BH. Select straight lines AG and BH, select [Intersection] in the [Construction] menu, and make the vertical center J.

Select points A and J, select [Line Segment] in the [Construction] menu, and make line segment AJ. Select line segment AJ, select [Midpoint] in the [Construction] menu, and make For the midpoint K of line segment AJ, use the same method to draw the midpoints L and M of line segments BJ and CJ.

Select points L and G, select [Line Segment] in the [Construction] menu, make a line segment LG, select the line segment LG, construct the midpoint, select [Vertical] in the [Construction] menu Line], draw the vertical bisector i of the line segment LG, and use the same method to draw the vertical bisector j of the line segment EF. Select the line segments LG and EF, select [Intersection] in the [Construction] menu, and make the center O of the nine-point circle. Select points O and E, and select [Construct a circle with the center and points on the circumference] in the [Construction] menu. Make a nine-point circle O.

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