Triangle Ratios
From Mycoted
A circle has an equilateral triangle touching it's circumference on the outside and another equilateral triangle touching its circumference on the inside, as pictured. What is the ratio of the areas of these two triangles?
Answer  

You don't need to do any complicated maths, if you rotate the inner triangle by 180 degrees it should become obviously guickly that the ratio is 1:4. 
