STEP 1: Begin with a triangle, and construct the perpendicular bisectors
of its sides. Mark the intersection point of the three perpendicular bisectors
as "circumcenter". Create points at the midpoints of each side
and hide the perpendicular bisectors. See picture below.
STEP 2: Now construct the altitudes from each vertex, and construct points
at the feet of the perpendiculars. Label the point of intersection of the
altitudes as the "orthocenter". Hide the altitudes. See picture
below:
STEP 3: Next, construct segments from the the orthocenter to each vertex,
and find the midpoints of these segments. Hide the segments, leaving only
the midpoints. See picture below.
STEP 4: Finally, construct the segment between the circumcenter and the
orthocenter, locate its midpoint, and hide the segment. This point is the
center of the nine point circle. Construct a circle with this point as the
center, and any of the nine points as the other point Using the circle by
center + point function under the construct menu).
