<p>An interesting twist is to look at the problem of a circle with radius 1 that is inscribed in a square. Such problem would be trivial for most SAT takers because the diameter also represents the value of one side. Hence, the area of the square is 4. What is the perimeter? 2 times 4 or 8. Hmm, the value for the area is one half of the value for the perimeter?</p>
<p>Could it be that the principles are the same, but that students are more used to see the relations between a square and a circle? </p>
<p>A further interesting twist would be to see what happens if the triangle was given and we needed to find the relationship with a circle that circumscribes the triangle. :)</p>