This article is the third in a series of activities that discusses some interesting relationships with triangles. The first article (EJ1259412) introduced the various circles and centres involved with a triangle, as well as the Euler Line (named after the famous mathematician Leonhard Euler) which passes through four of the five centres. The…

This article is the fourth in a series of activities that discusses some interesting relationships with triangles. Brian Sherman shows an activity demonstrating Euler's Theorem, which gives the distance from between the circumcentre and the incentre of a triangle.

This article is the second in a series of activities that discusses some interesting relationships with triangles. Brian Sherman shows how to determine the altitudes of a triangle, its area, and the lengths of its circumradius and inradius. [For the first activity in the series, see EJ1259412.]

This article is the first in a series of activities that discusses some interesting relationships with triangles. Brian Sherman shows how to find five centres for a triangle--the circumcentre, the incentre, the orthocentre, the centroid and the nine-point centre, with four of the five to be found on the Euler line. With these centres, he shows…