Gsp5 construct circumcenter5/12/2023 What do you observe?ħ.) We construct the centroid - the intersection of the medians. What can you say about the orthocenter, the center of the nine-point circle, and the circumcenter?Ħ.) We draw the medians - the segments that connect the three vertices to the midpoint of each side. We find other interesting points on the circle.ĥ.) We construct a circumcircle –– a circle passing through vertices of the triangle and find its circumcenter (the center of the circumcircle). The circle is what we call the nine-point circle. To do this, just select the Circle through Three Points tool, and then click any three of the nine points.Īs we can see, the nine points are indeed on a circle. Using the pointer tool from your toolbar on the left hand side, you will choose an angle of your triangle by. Using GeoGebra, we can verify if the nine points mentioned above lie on a circle. Example: Construct a triangle, given the circumcenter O, the center of the nine-point circle N, and the midpoint of one side A. Now it is time to create the angle bisectors. The red points are the midpoints of each side, the green points are the ‘foot’ of each altitude, and the cyan points are the midpoints of the orthocenter and and the vertices.įrom the figure above, we observe two things: first, the altitudes seem to meet at a point and second, it seems that the 9 points form a circle (can you verify this by construction?). figures impossible to construct under the traditional compass-and-straight-edge rules (such as the. For the sake of discussion, we color the points. caption Geometers Sketchpad editing a circumcircle. What do you observe about the nine points?Īfter finishing the steps above, your figure should at look like Figure 1. What do you observe? The intersection of the altitudes is called the orthocenter.Ĥ.) Construct the three midpoints between the orthocenter and the three vertices.
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