/sci/ - Science & Math

Allow the vertices of an 'inscribed' triangle to fall on the extended sides of the outer triangle, so in the picture shown the blue triangle is 'inscribed' in the red triangle.

Then, given any two triangles such that the first is 'inscribed' in the second, show that there exists a third triangle which completes a 'loop' of triangles, each one 'inscribed' in the next. How many triangles can complete the 'loop'?