Click on the blue points and drag them to change the figure.
In what cases is the point of concurrency inside the triangle. In what cases is the point of concurrency outside the triangle. In what cases is the point of concurrency on the perimeter of the triangle?
 Manipulative 1  Perpendicular Bisector Concurrence Theorem Created with GeoGebra. 

The Perpendicular Bisector Concurrence Theorem
proves that, for all triangles, the
perpendicular bisectors
of the sides of a triangle are
concurrent
at the
circumcenter
of the
triangle.
If one draws any triangle, then draws the perpendicular bisectors of the sides,
all three perpendicular bisectors will meet at the same point. When two or
more lines meet at the same point, they are said to be concurrent at that
point. Furthermore, if one draws a circle with the center at the point of
concurrency and the edge through any of the vertices of the triangle, it
will also pass through the other two vertices. This circle is called the
circumcircle of the triangle. For a proof of the Perpendicular Bisector
Concurrence Theorem,
see Proving the Concurrency of the Perpendicular Bisectors of a Triangle, By Sharon K. O’Kelley.
