This applet displays the relationship between the four primary "centers" of a triangle. To change the triangle, drag any of the three corners (vertices). [list] [*]The Incenter is located at the point of concurrency (intersection) of the angle bisectors. [*]The Circumcenter is located at the point of concurrency of the perpendicular bisectors. [*]The Centroid is located at the point of concurrency of the medians. [*]The Orthocenter is located at the point of concurrency of the altitudes. [/list] You can also display the circumcenter (the smallest circle that will fit around the triangle), the incenter (the largest circle that will fit inside the triangle), the Euler line (the line that three of the centers always fall on), or the midsegments.
1. Which one of the centers is equidistant from each corner (vertex) of the triangle? 2. Which one of the centers is equidistant from each side of the triangle? 3. Which one of the centers does not always lie on the same line as the other three? 4. Which two of the centers can be outside of the triangle? 5. What is the ratio of the midsegment to its parallel triangle side?