Clover Problem
A four-leaf clover consists of 4 coplanar circles. The large circular leaves are externally tangent to each other, as well as to each of the smaller circular leaves, which are also congruent to one another. The radius of the large and small circular leaves is 1 1/2 inches and 1 inch, respectively. What is the area of a rhombus formed such that each of its vertices are also the center of one of the four circular leaves?
Hint 1
- One of the ways to find the area of a rhombus is to take half the product of the diagonals.
A= ½ (d1)(d2)
Hint 2
The radius of each large circular leaf is 3/2 inches. That makes the length of the shorter diagonal 3 inches. If we include this diagonal in the figure we can see that two isosceles triangles are formed.
Hint 3
The altitude of the isosceles triangle is half of the longer diagonal (n). Also the hypotenuse of the right triangle created by n is equivalent to the sum of the smaller radius and the larger radius.