Start with any triangle. Take the centre point of the side of the triangle, and rotate the two halves of this side about this centre point, until they are each parallel with the side they were originally connected to at a vertex, then repeat this for all sides of the triangle. All the endpoints of these rotated half sides will be on a Circle. Pairs of them will be on a line with the vertex between them. Each of these lines will be the bisector of the External angle between the two sides that meet at that vertex. All of these bisectors meet at points which are the centres of the Excircles of the triangle.