Three equal circles of unit radius touch each other. Then, the area of the circle circumscribing the three…

Question

Three equal circles of unit radius touch each other. Then, the area of the circle circumscribing the three circles is

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Three equal circles of unit radius ( $r=1$ ) touch each other. We need to find the area of the circle circumscribing these three circles.

Determine the arrangement of the three circles.
When three equal circles touch each other, their centers form an equilateral triangle. Since the radius of each circle is $r=1$ , the distance between the centers of any two touching circles is $2r = 2(1) = 2$ . Thus, the side length of the equilateral triangle formed by the centers of the three circles is $a = 2$ .
Find the radius of the circumscribing circle.
The center of the circumscribing circle will coincide with the

Three equal circles of unit radius touch each other. Then, the area of the circle circumscribing the three circles is