Perpendicular Bisectors of Triangles
Below is a triangle with all 3 of its sides' perpendicular bisectors being shown.
Drag the vertices of the triangle to create a variety of triangles, and see what you notice.
Use the questions below to help guide your exploration and then answer each of them with your findings.
Do all of the perpendicular bisectors meet at a point? (Check to see if this is always true by dragging the triangle's vertices.)
Will that point (point C) always be located inside of the triangle? Why or why not?
What can you conclude about the location of point C based on the type of triangle (acute, obtuse, right)?
Do you notice anything interesting about point C in relation to the circle that the triangle in contained in?