Triangle+Center

Triangle Centers

 * Incenter**
 * intersection of __angle bisectors__
 * Center of inscribed circle (equidistant from sides)
 * Always inside the triangle
 * Circumcenter**
 * intersection of __perpendicular bisectors__
 * Equidistant from vertices
 * In right triangles, lies on midpoint of hypotenuse (relationship between circumcenter and center of a circumscribed circle about the triangle?)
 * Centroid**
 * Intersection of __medians__
 * Always inside the triangle
 * Each median divides into triangles of equal area (think ratio of areas- same height, and now same base)
 * Divides median into segments that are 2:1- essentially, the centroid is always 2/3 of the way down the median
 * Also center of mass/balance (cool trick- you can balance index card figure on pen at the centroid)
 * Orthocenter**
 * Intersection of __altitudes__
 * Not always in the center- outside of the triangle is obtuse

Circumcenter, centroid, and orthocenter are collinear- called the Euler Line