A circle is circumscribed about an equilateral triangle, and another circle is inscribed in the triangle.

Question

What is the ratio of the are of the larger circle to the area of the smaller circle?

Here is the link to the figure. Please remove the space before docs and after document

https:// docs.google.com/document /d/18WA9M3kD4-RxT7V9JJxIH9X3kM3OIhJCeYalqSDfVnY/edit?usp=sharing

Answer 1

Let R = radius of the larger circle; the area is πR²

Let r be the radius of the smaller circle.

r is the shorter leg of a 30-60 rt triangle with hypotenuse R, i.e. r = R/2; the area is πR²/4

A(R)/A(r) = 4