__Category__: Plane Geometry, Algebra"Published in Newark, California, USA"

Each of the four circles shown in the figure is tangent to the other three. If the radius of each of the smaller circles is x, find the area of the largest circle. If x = 2.71, what is the area of the largest circle?

Photo by Math Principles in Everyday Life |

__Solution__:

Photo by Math Principles in Everyday Life |

Consider the equilateral triangle, draw the perpendicular lines from each vertex, and label further as follows

Photo by Math Principles in Everyday Life |

In a 30° - 60° - 90° triangle, the shortest side is half of the hypotenuse which is ½ y. The other side of a triangle is equal to the shortest side times the square root of three. Therefore, we can solve for the value of y in terms of x as follows

or

The radius of a big circle is

Therefore, the area of a big circle is

If x = 2.71, then the area of a big circle is