The CENTROID of a triangle is the typical intersection of thethree medians. A typical of a triangle is the segment indigenous a vertex come themidpoint of the contrary side.

You are watching: Is the incenter equidistant from the vertices

Click ~ above the photo to open up theGSP record to discover what wake up to the figure as you drag among the vertices.

Notice that the centroid is alwayson the inside of the circle.

The ORTHOCENTER the a triangle is the typical intersection of thethree present containing the altitudes. An altitude is a perpendicular segmentfrom a vertex come the heat of the contrary side.

Click top top the an initial picture to openthe GSP paper to explore what happens to the number as girlfriend drag among thevertices.

Notice the the orthocenter issometimes exterior the triangle, occasionally on the triangle, and also sometimes insidethe triangle.

The CIRCUMCENTER that a triangle is the point in the planeequidistant native the three vertices the the triangle. Since a point equidistantfrom 2 points lies top top the perpendicular bisector the the segment figured out bythe two points, the Circumcenter is top top the perpendicular bisector of each sideof the triangle.

Click top top the an initial picture to openthe GSP file to discover what wake up to the number as girlfriend drag one of thevertices.

Notice that the Circumcenter isalso sometimes outside the triangle and also sometimes within the triangle.

The INCENTER the a triangle is the allude on the internal of thetriangle the is equidistant indigenous the 3 sides. Since a allude interior come anangle the is equidistant from the 2 sides the the edge lies top top the anglebisector, then the Incenter must be on the edge bisector of each angle that thetriangle.

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Click on the picture to open up theGSP file to explore what happens to the number as girlfriend drag among the vertices.