Krishna
0

Step 1: Recall the formulas of the radius of the circumscribed circle and the radius the inscribed circle.

             NOTE: If R is the radius of the circumscribed circle and r the radius the

                          inscribed circle to an equilateral triangle of side a,

              FORMULAS:   r = a *\frac{\sqrt{3}}{6}

                                     R = a *\frac{\sqrt{3}}{3}


Step 2: Find the ratio of the area of the circumscribed circle to the area of the inscribed circle.

            NOTE:  \frac{Area\ of\ the\ circumscribed\ circle}{Area\ ofthe\ inscribed\ circle.}

                        = \frac{\pi * R^2}{\pi* r^2}  

                        = \frac{R^2}{r^2}


Step 3:  Write the formulas for R and r and simplify

              NOTE:  =   (\frac{a*\frac{\sqrt{3}}{3}}{\frac{\sqrt{3}}{6}})^2

                          = (\frac{6}{3})^2

                          = 4