This morning I decided to demonstrate how to use a compass and straight rule to find the incenter of a triangle.

This is a relatively easy task, especially given this rather cool way of bisecting an angle.

To construct this diagram, simly draw out a triangle:

Draw two concentric circles on two vertices:

Join each alternate segment like so:

Draw a line that from the vertex through the intersection:

Where they meet is the incenter. (incentre for UK?!)

Then colour it in for a laugh: