Finding the Circumcenter Use Geogebra to construct a point the same distance from three given points.
Vocabulary:
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Noncollinear: points not on the same line
Circumcenter: the point equidistant from three noncollinear points.
Technology:
Geogebra is a free interactive application used for graphing algebraic equations and constructing
geometric figures.
Steps of Lesson:
1. Use Geogebra to place a map under insert image.
2. Mark a point on three noncollinear cities (cities not on the same line) and then form a triangle
connecting the points.
3. Construct the perpendicular bisector for each side of the triangle by choosing the line bisector
option. Students may also construct the perpendicular bisector with a compass and straight
edge, if working on paper. The point where the perpendicular bisectors intersect is called the
circumcenter.
4. Place a point at the intersection for perpendicular bisectors. To illustrate that the
circumcenter is the same distance from the three original points, construct a circle with the
center at the circumcenter and a point on the circle as one of the cities.
5. The circle will pass through the three cities, showing that the radius length is consistent from
the circumcenter to the cities.
6. Change the location of the cities and observe.
Extension:
If the three cities form and acute triangle, then the circumcenter is inside the triangle.
If the three cities form a right triangle, then the circumcenter is the midpoint of the hypotenuse of
the right triangle.
If the three cities form an obtuse triangle, then the circumcenter is locate outside of the triangle.
North Carolina Geographic Alliance http://geo.appstate.edu/NCGA