6.2 Circumcenter and Incenter

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Presentation transcript:

6.2 Circumcenter and Incenter

Open a new Geogebra File Construct a triangle. Construct the perpendicular bisector of each side of the triangle. Construct a circle with the center at the point of concurrency through one of the vertices of the triangle. Make a conjecture.

Concurrency – Three or more lines that meet at a single point.

4 Points of Concurrency Circumcenter Incenter Centroid Orthocenter

Circumcenter The point of concurrency of the perpendicular bisectors of each side of a triangle. It is equidistant to the vertices of the triangle.

Open a new Geogebra File Construct a triangle and find the incenter, which is the point of concurrency of the angle bisectors. Make a conjecture about the center. (Hint, use a property of angle bisectors)

Incenter Point of concurrency of the angle bisectors. It is equidistant to the sides of the of a triangle.

Geometers Sketchpad.

You must use Geogebra to answer the following: Turn on Axes and Gridlines. Aves go vertically, Streets go horizontally. Starbucks has three coffee shops in Lower Manhattan. One is located on the corner of 4th Ave and 4th Street, the second is located on the corner of 8th Ave and 16th Street and the third is located on 2nd Ave and 14th street. Find where Starbucks should put their coffee been storage facility so that it is as close as possible to all three coffee shops.

You must use Geogebra to answer the following: Open up the Geogebra File titled “6.2 In Class Problem” The line segments AB, BC and AC represent bike paths in central park. The city wants to place a mechanics stand so that people can fix their bikes at the park. Find the best location as an ordered pair for the mechanic stand so that it is an equidistant walk from each of the paths.

Review other special segments of a triangle.