Explorations in Geometry
Here is another little ditty from John H Conway. This one may be a New theorem. Follow these directions to see if you can discover it for yourself.
1) create a triangle ABC
2) Extend sides AB and AC from point A a distance equal to length BC
3) Extend sides BC and BA from Point B a distance equal to AC
4) Extend sides CA and CB from Point C a distance equal to AB
5) Find a relationship between the six points so created E,F, H,K,M,N
they ALL have something in common.
6) What else can you observe about this figure
7) Did you notice anything about the INCENTER of the triangle? Look
8) Write a brief paragraph and describe the relationships you have observed in this exploration.