Three circles of radius 5 are drawn so that each touches the other two. Find the radius R of the outer circle that touches all of the three circles, as shown in the figure below.
+128406 If we join the ceters of these circles, we have an equilateral tirangle with sides of 10
We can compite the distance, D, from the center of the large circle to the center of any of the small circle as
10^2 = 2D^2 - 2D^2 cos (120°)
100 = 2D^2 - 2D^2 (-1/2)
100 = 3D^2
100/3 = D^2
D = 10/sqrt (3)
So....the radius of the larger circle is 10/sqrt (3) + 5 ≈ 10.774
