What is the difference between centroid and circumcenter

Since H is the orthocenter, H is on DM by the definition of orthocenter. Therefore, DM meets EF at a right angle. Construct a line through points C and G so that it intersects DM. However, this has not been proven yet. So, label the point of intersection H'. Construct CX. Thus, G , H' , and C are collinear. The centroid is the center of a triangle that can be thought of as the center of mass. It is the balancing point to use if you want to balance a triangle on the tip of a pencil, for example.

If you have Geometer's Sketchpad and would like to see the GSP construction of the centroid, click here to download it. The circumcenter is the center of the circle such that all three vertices of the circle are the same distance away from the circumcenter. Thus, the circumcenter is the point that forms the origin of a circle in which all three vertices of the triangle lie on the circle.

Thus, the radius of the circle is the distance between the circumcenter and any of the triangle's three vertices. It is found by finding the midpoint of each leg of the triangle and constructing a line perpendicular to that leg at its midpoint. Where all three lines intersect is the circumcenter. The circumcenter is not always inside the triangle. In fact, it can be outside the triangle, as in the case of an obtuse triangle, or it can fall at the midpoint of the hypotenuse of a right triangle.

This is the center of a circle, called an excircle which is tangent to one side of the triangle and the extensions of the other two sides. Naturally, every triangle has three excenters and three excircles. The Euler line of a triangle is the line that passes through the orthocenter , the circumcenter , and the centroid. It also contains the center of the Nine Point Circle.

Java images created using Cinderella by Scott Sutherland on March 12, The four arcs create two points of intersection on either side of the segment. Draw a line joining these two points with the aid of the ruler, and that will give the perpendicular bisector of the segment. To create the circumcircle, draw a circle with the circumcenter as the center and the length between circumcenter and a vertex as the radius of the circle. Incenter: Incenter is the point of intersection of the three angle bisector s.

Incenter is the center of the circle with the circumference intersecting all three sides of the triangle. To draw the incenter of a triangle, create any two internal angle bisectors of the triangle. The point of intersection of the two angle bisectors gives the incenter.

To draw the angle bisector, make two arcs on each of the arms with the same radius. This provides two points one on each arm on the arms of the angle.

Then taking each point on the arms as the centers, draw two more arcs.