Incenter, Orthocenter, Circumcenter, Centroid. Date: 01/05/97 at From: Kristy Beck Subject: Euler line I have been having trouble finding the Euler line. Orthocenter: Where the triangle’s three altitudes intersect. Unlike the centroid, incenter, and circumcenter — all of which are located at an interesting point of. They are the Incenter, Orthocenter, Centroid and Circumcenter. The Incenter is the point of concurrency of the angle bisectors. It is also the center of the largest.

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Construct the median DX.

The orthocenterthe centroid and the circumcenter of a non-equilateral triangle are aligned ; that is to say, they belong to the same straight line, called line of Euler. Orthocenter, Centroid, Circumcenter and Incenter of a Triangle. Centroid Draw a line called a “median” circujcenter a corner to the midpoint of the opposite side.

## Triangle Centers

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 circumcenter, click here to download it. The orthocenter H of a triangle is the point of intersection of the three altitudes of the triangle.

The radius of the circle is obtained by dropping a perpendicular from the incenter to any of the triangle legs. An angle bisector is a line whose points are all equidistant from the two sides of the angle.

### Triangle Centers

The incenter is the last triangle center we will be investigating. There are several special points in the center of a triangle, but focus on four of them: The angle bisectors of a triangle are each one of the lines that divide an angle into two equal angles. You see the three medians as the dashed lines in the figure below. The centroid is the center of a triangle that circu,center be thought of as the center of mass. The circumcenter is the center of a triangle’s circumcircle circumscribed circle.

Draw a line called a “median” from a corner to the midpoint of the opposite side.

It is constructed by taking the intersection of the angle bisectors of the three vertices of the triangle. The line segment created by connecting these points is called the median. The centroid of a triangle is constructed by taking any given triangle and connecting the midpoints of each leg of the triangle to the opposite vertex. The incenter is the point of intersection of the three angle bisectors. Thus, the incenter I is equidistant from all three sides of 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.

### Math Forum – Ask Dr. Math

The incenter is the center of the circle inscribed in the triangle. Let X be the midpoint of EF. Where all three lines intersect is the center of a triangle’s “circumcircle”, called the “circumcenter”: Orthocenter Draw a line called the “altitude” at right angles to a side and going through the opposite corner. Like the circumcenter, the orthocenter does not have to be inside the triangle. The incenter I of a triangle is the point of intersection of the three angle bisectors of the triangle.

Therefore, DM meets EF at a right angle. If you have Geometer’s Sketchpad and would like to see the GSP construction of the orthocenter, click here to download it.

The circumcenter is not always inside the triangle. The circumcenter is the center of the circle such that all three vertices of the circle are the same distance away from the circumcenter.

The circumcenter C of a triangle is the point of intersection of the three perpendicular bisectors of the triangle. The altitude cenrroid a triangle is created by dropping a line from each vertex that is perpendicular to the opposite side.

Draw a line called a “perpendicular bisector” at right angles to the midpoint of each side.

A perpendicular bisectors of a triangle is each line drawn perpendicularly from its midpoint. The centroid G of a triangle is the point of intersection of the three medians of the triangle.

Incenter Draw a line called the “angle bisector ” from a corner so that it splits the angle in half Where all three lines intersect is the center of a triangle’s “incircle”, called the “incenter”: You can look at the above circucenter of an circumcenteer triangle, or the below examples of an obtuse triangle and a right triangle to see that this is the case. Draw a line called orfhocenter “altitude” at right angles to a side and going through the opposite corner.

Like the centroid, the incenter is always inside the triangle. The centroid divides each median into two segmentsthe segment joining the centroid to the vertex is twice the length of the length of the line segment joining the midpoint to the opposite side.