NCGA GeoMath Lesson Plan
Name of Lesson
Finding the Circumcenter
Time for Instruction
20-25 minutes
Essential Question(s)
If given three locations on a map, determine the point equidistant from those three locations?
Common Core Standard(s)
Make geometric constructions
Make formal geometric constructions with a variety of tools and methods (compass and
straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).
Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing
perpendicular lines, including the perpendicular bisector of a line segment; and
constructing a line parallel to a given line through a point not on the line.
National Geography Objective(s)
8 grade 1
3. Geospatial technologies—Internet-based mapping applications, GIS, GPS,
geovisualization, and remote sensing—can be used to construct geographic representations
using geospatial data
Prerequisite skills/knowledge
Construct a perpendicular bisector with a compass and straightedge as well as using mathematical software.
Insert a background image into the mathematical software called Geogebra.
Anticipatory Activity/Bellringer/Warmup
Place a large map in the front of the room with three cities marked. As students enter the classroom, ask them to
place a small post-it note or sticker of the location that they foresee as equidistant from the three cities. Choose
three cities that form an obtuse triangle when connected for the most diverse predictions.
Mathematical Terms
Geography Terms
Perpendicular Bisector
Instructional Strategies/Sequence
Using Geogebra, place points to represent three cities and then complete the process to locate the circumcenter.
Drag the points to create multiple types of triangles: acute, right, obtuse, and observe the location of the
Independent Practice
Change the location of the cities and observe the corresponding change of the circumcenter.
Instructional Resources
Formative Assessment
Students should locate another map and construct the circumcenter. Include the circle to illustrate that the
circumcenter is equidistant from the three cities. Export the screen image to the program’
Complete the same procedure with a compass and straight edge
Write conditional statements (if/then statements) to model the location of the circumcenter for cities that form
acute, right and obtuse triangles. For example, if three cities form an obtuse triangle, then the circumcenter is
located outside of the triangle.
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.