Centers of a Triangle

Given a triangle ABC there are several natural centers you can show in this sketchpad. Sorry, this page requires a Java-compatible web browser.

Symbols
O - CircumCenter G - Centroid H - OrthoCenter
K - Lemoine Center N - Nine Point Center I - InCenter

Definitions
O - The center of the circumscribed circle can be found as the intersection of the perpendicular bisectors of the sides.

G - The centroid is the intersection of the medians.

H - The Orthocenter is the intersection of the altitudes.

K - The Lemoine point is the intersections of the symedians. The external symedians are the tangent lines to the circumcircle at the vertices, and can be used to construct the Lemoine point since the symedians are the lines connecting a vertex and the intersection of the two opposite external symedians.

N - The Nine point center is the center of the Nine point circle, which is the circle containing three Midpoints Ma, Mb and Mc, the three altitude base points Ha, Hb and Hc as well as the three Euler points Ea, Eb and Ec. N can be found as the midpoint between the H and O. The line through H and O is called the Euler line. G is also on the Euler line.

I - The center of the inscribed circle can be found as the intersections of the angular bisectors at each vertex.

Symbols
O - CircumCenter	G - Centroid	H - OrthoCenter
K - Lemoine Center	N - Nine Point Center	I - InCenter

Definitions
O -	The center of the circumscribed circle can be found as the intersection of the perpendicular bisectors of the sides.
G -	The centroid is the intersection of the medians.
H -	The Orthocenter is the intersection of the altitudes.
K -	The Lemoine point is the intersections of the symedians. The external symedians are the tangent lines to the circumcircle at the vertices, and can be used to construct the Lemoine point since the symedians are the lines connecting a vertex and the intersection of the two opposite external symedians.
N -	The Nine point center is the center of the Nine point circle, which is the circle containing three Midpoints Ma, Mb and Mc, the three altitude base points Ha, Hb and Hc as well as the three Euler points Ea, Eb and Ec. N can be found as the midpoint between the H and O. The line through H and O is called the Euler line. G is also on the Euler line.
I -	The center of the inscribed circle can be found as the intersections of the angular bisectors at each vertex.

This is a prototype of JavaSketchpad, a World-Wide-Web component of The Geometer's Sketchpad. Copyright ©1990-1997 by Key Curriculum Press, Inc. All rights reserved. Portions of this work are being funded by the National Science Foundation (awards DMI 9561674 & 9623018).